they can catch human colds, me & my old jill spent a whole month alternately snotty, i gave her the cold, i got better, she gave it back to me, she got better
just keep em warm, plenty of soft grub (you know what it's like trying to eat with a blocked up nose!).
steer clear of sawdust as bedding, 2 of mine are allergic to it, one got absolutely covered in scabs when my dad cleaned him out & bedded them on it, scratched himself raw, poor little bugger.