What to do with a frozen bike?
Let it air dry (and/or wipe it dry as much as you can) and move on with your life. Don't put it near a heater, cause that isn't good for the rubber stuff. Re-lube the chain. 

What gets you in winter is not so much the snow/ice, but the salt (which doesn't affect your bike if its just standing there). In this case, if you have the time and space to bring the bike in for a prolonged period of time (say, overnight), you can wipe down the frame with a damp cloth, maybe clean+lube the chain and drivetrain and other parts you would do routinely (e.g. brake pivots if you're using V-brakes; I usually have to take the v-brakes off and clean the posts and what not at least a few times in a winter). 

Also, note that you can't rust out an aluminum bike, and this shouldn't really have caused a problem for a steel bike. A lot of people have bikes (steel or otherwise) which they leave out through winters and salt and survive fine for decades.