They can certainly get what the vet calls, " upper respiritory infection," which to my mind is the same as a cold.
Sometimes mine have ended up with the sniffles when I've been suffering with a cold.
I think you're doing the best thing by trying to keep away from them, you can never be too careful with small puppies, no point taking unecessary risks.
Especially with the hand washing, they say you catch most colds from picking up germs from door handles etc then touching your face!
