Oooh I see. I ride in the Winter, of course *just not in freezing temperatures* - and when I do, I use my Bit Warmer. I stick it in the nooker for a few mintues and then wrap it around my bit. It hangs on my bit while I catch him, groom him, tack him up and by the time it is ready to go into his mouth, it is nice and warm for him.
I used to warm it up with my hand, but that sucks in the cold. Once I put my winter riding gloves on, I don't want to have to take them off to warm my bit.
So the Bit Warmer comes in handy :)
Now, with the bit sticking to their lips or tongue, I have never seen it happen - but again, I don't ride my horse in the freezing temperatures. I don't think it would happen though - good question!