YES CURLYCORIANDER! I cannot stress enough that cold weather + wet hair DOES NOT cause a cold or the flu or anything. So many people have this misconception because of what our mothers told us! If there is a virus or bacteria that our body cannot fight off, you will show symptoms whether your hair is wet or dry.
If you're worried about leaving the house with a wet head and being cold and uncomfortable, you could probably use a diffuser to partially dry your hair. Depending on your hairstyle, you could wear a hat, or a headwrap or something.