When practicing I can go straight from warm hands (e.g. on a radiator or a cup of tea) to the piano and then, with hands already warm in that sense, I can warm up with a few scales and maybe a bit of improv (at which I am rubbish) or chord voicings etc. before starting on the first piece. After that I'm warmed up for all playing thereafter.

If I come to the piano with cold hands and try to play properly immediately I can't do it at all well, and in this I suspect I am by no means alone. The problem is that when you play in a competition or festival (or even at my lesson come to that) this is exactly what you are expected to do, especially when they specifically say (as they often do) that there is no room with a piano to warm up on, hence the question:

How do you go from sitting waiting (possibly with cold hands) to playing without warming up at a piano? What do you do?

I start with a piece that is bold, medium paced, not requiring any subtle dynamics or nuances of touch, that lasts 3 or 4 minutes, and that I know absolutely inside out. All of that means that it is possible to make a reasonable job of it with hands that are not yet loosened up, and by the end of it they are ready for something more demanding. it also helps to settle the nerves.

I have been told by my teacher to put a scarf around my hands to warm them up naturally. She told me never to use hot water or heat them up on a radiator to warm them up as it would affect the muscles in my hands and would affect my playing.
Well I'm not good enough to have noticed any difference but knowing her musical background and having heard her play I always take her advise as gospel truth!!!

Gloves! (Sometimes I play wearing a fingerless pair too.)

Mittens are good too for warming the hands because the body heat from your fingers helps to warm the fingers too.

You could try those handwarmer things you can get from campling shops. (the ones where you press the button and it creates a chemical reaction).

My piano lessons are in the morning and about half an hour away in the car, so I wear really thick mittens and keep my hands warm on the heaters in the car, I've tried playing with cold hands and it's not good!

I often wear fingerless gloves-my piano's out in the conservatory, and in the winter, it's usually as cold in the conversatory as it is outside! Scales and things warm up my hands in the muscular sense, but I swear by fingerless gloves otherwise.

I always put my hands under my top, together with my recorders (clearly you can't do this with a piano....) - it's a question of bringing my fingers up to my own core temperature, and is the only way I know reliably to warm them. Hot water simply sends the cold up your arms, and then once you take your hands out, it seems to seep right back down again (and no, I know it doesn't match what the anatomy should be doing, but it does seem to do that). In winter I never travel to a venue without wearing gloves, either.

I don't find playing directly before a performance that helpful, except to get a few tuning notes sorted out - I find that nerves are at their peak, and I generally want to avoid doing anything to make them worse (ie mistakes!). I'll focus instead on thinking about the first few phrases of the first piece, to set an internal pulse - and generally would organise a programme to have a less challenging piece first in order to do the rest of the warming up that way.

I sometimes practise like this. I once practised in a pair of proper gloves, but only played half a piece because it didn't work!

I plan my programme to allow for cold fingers in the first few minutes of each half and work up to the most difficult pieces so I finish the first half, and the concert, on the pieces requiring warm toasty hands!

I'm sure I read somewhere that Glenn Gould plunged his hands into "boiling" (I think he meant very hot!) water prior to performing. This is what I did when I took Grade 8 one November in what appeared to be an unheated shed (actually, the Music School at Cheltenham Ladies' College!). Your comment that Hot water simply sends the cold up your arms, and then once you take your hands out, it seems to seep right back down again sounds well bizarre to me and doesn't chime with my experience - maybe you have an unusual vascular system!

I think that there are two separate issues here. Firstly, it is essential to have warm hands before starting to play and secondly, the internal apparatus associated with playing needs to be as "warm" as possible. The act of "warming up" at the piano refers to not so much to increasing the temperature of the hands as to the business of warming up the reflexes, hearing and getting the experience of the body/brain in an optimal state to play.

To address the thermal problem, I find that those activated charcoal thingies you buy in camping shops are brilliant and can be shoved into gloves or preferably mittens. For the other sort of warming up, you need to develop a drill which gets all aspects primed. It is also essential to be able to play without warming up and this should be practised like all other aspects of performance. So practise just going to the piano and starting with no preparation. Never, however play with cold hands.

Changing the subject somewhat, how does your piano cope in a conservatory?!

Okay, if you want a more mechanical description, steeping arms in warm water will warm the outer layer of skin first, and take much much longer to warm the underlying muscle, which is what actually needs to be warm in order to play properly. Take your arms out, and the superficial tissue then loses heat back to the atmosphere again, and because that is cooler than your core temperature will be, the general direction of heat transfer will be straight back outwards again, more so than in towards the muscle. End effect, muscles still cold. Remember too that the muscles controlling flexion and extension of fingers are located in the forearms (I know I'd be attempting to teach the OP to suck eggs on this one, but for those who haven't studied anatomy!), hence my going on about arms and not just hands. In the case of hypothermia, one management is to put the victim into a warm bath, but in that case the limbs should be left dangling out, or they send their cold contents winging straight back into the body's core, which is more dangerous still, as the peripheries tend to get colder than the central core does.

I'd still advocate using your own core warmth as the best way to ensure hands and forearms are warm enough to play: having tried warm water and radiators at various times, I've tended to find my limbs warming up a little, then stiffening again early in the playing process as a general feeling of coldness reasserts itself. Wearing enough clothing for as long as possible before a performance, and having warm clothes to perform in in winter is also important in this.

Hand warmers!

... also useful in pockets for orchestral players playing in cold churches for a quick hand-re-warm during long rests!

The disposable ones generally stay warmer longer and are lighter (good for longer gigs) but heavier (less discreet in pockets) and work out more expensive if you use them a lot.

For regular use get the re-heatable plastic ones , there are some fun-shaped ones around (although I've never come across a piano one )

Failing all else..... coffee in a flask and a disposable cup to warm your hands on.....

It's a digital, sorry, I should have said that

And Grainger said to slap your hands on your thighs repeatedly for 5 minutes. (He of course was not at all bothered what people thought of him...)

Well slap my thigh and call me Sally!

I sit on my hands (sometimes wearing gloves) in the car on the way to exams/performances. However, that's a bit difficult if I'm 'arranging own transport' rather than relying on my parents' taxi service - I have to cycle!

First, here's what my teacher said: Firstly, make sure you are warm enough internally so that you don't feel cold and your hands are reasonably warm - wear gloves, have a heater etc. Then rub your palms together vigorously until the palms are hot. Then massage each finger individually to get the blood flowing. About 5-10 minutes before the performance eat a chocolate. Spend the last few minutes dummy/ghost playing, on a flat surface if you can or in mid air or on your thigh otherwise, to get the muscles going.

I think there are a couple of points here:

Body temperature is not a fixed as some people think - it isn't 37 degrees all the time for everybody. In particular a lot of muscles work optimally at a slightly higher temperature - perhaps as much as 40 degrees or more (the core temperature of endurance athletes can level out to about 42 degrees once warmed up). However, the body is very good at dissipating heat so the only way to get the muscles to a higher temperature and maintain it is to generate the heat within the muscles. The only way to do this is by using them. Consequently using the required muscles is an absolutely essential part of warming up. It helps if your starting point is as high as possible so be normally warm to start with. As for the Chocolate, it has been said that one reason people feel good after eating chocolate is that it contains chemicals with a direct pharmacological effect to that end and it can only do good before performing. Also, I imagine the sugar rush can't do any harm.

Second, The bit of the festival I entered was yesterday. I did what she said. Due to a problem at work I only arrived at the venue 1 minute before my first class was due to start but I was second on so I had time to recover. Having run from the car park I was warm, but the gap before my performance meant I could do all the things she said. I played in the classical section first (played well but the adjudicator didn't like the style), then the Bach class an hour later, then the Romantic composer class after that. Finished nowhere, first (of 2) and second (of 3) respectively. Having won the Bach class I now have to go back and play in the winners competition on Thursday. I've got no chance of winning (the girl who played a Rachmaninoff prelude in one class and won, a Mozart sonata movement in another and should have won and a Debussy Nocturne in another and won - all played to a wonderful standard) but that isn't why I'm there - it's the opportunity to play in front of an audience!