Do eggs have to be cold?

It depends. If you want to eat them, they should be refrigerated. If you want to hatch them, you should keep them warm.

If they're fresh, and haven't had the bloom washed off (a protective membrane) then you don't have to worry about refridgerating them (but they only last about 2 ish weeks if not refridgerated) but if they have already been refrigerated they must be kept cold.