If we go outside with wet hair, will we catch a cold?

"If you go outside with wet hair, you'll catch a cold!" Umm, no.

You can walk around completely naked with wet hair in the rain on a cold winter day without catching a cold or getting sick.
To catch a cold, you need to be exposed to a virus. As long as you haven’t been infected, there’s no reason you’ll wake up congested the next day.
In fact, you’re more likely to catch a virus indoors than when you’re out in the open air.

Wet hair can affect your body temperature, which might make your immune system slightly less effective than usual, but there’s no direct link between wet hair and catching a cold, of course.