I have a 98 Camry. The engine has absolutely no problem starting in cold weather, but everytime the car is shut off the radio resets. Would it be the battery? the radio itself? a disturbance in the force? I don't have a whole lot of knowledge about cars but I'm trying to learn more.

Original factory radio?

Yes, its the original Toyota radio.

If you are not the original owner, there is the possibility that the original radio had been replaced with something fancier then reinstalled at sale. Possibly the rewiring was not done correctly. Before you remove the radio to check, you might want to clean the battery connections and as many grounds as you can find and see if that helps.