(Like the others) I agree on the inconvenience of cold hands too! This probably sounds like 'obvious' advice, but have you tried warming your hands way before you enter the hall? Or stuffing them into your pockets/up your sleeves when you're not using them? You could also try doing little hand and finger exercises before the exam too! Staying hydrated is also a good way to keep the blood flowing, but the downside to drinking too much is you'll have to take bathroom breaks.
It's worthy to note that tension can make your hands cold too! It may not be that you're nervous or anything, but just that your hands haven't been doing much, or that something else is on your mind that your body is reacting to with stiffness.
Also, unfortunately, I don't think keeping an electric hand warmer in your pockets is allowed... but there's no specific rule saying that you can't, so as long as you don't take it out during the exam, it should be fine?
Ah, sorry this got a little long. I hope you can overcome this soon!