After soaking we dry his bottom by setting him on a paper towel right before putting him back in his enclosure. Usually leave the top wet, just dry the bottom so all the coco coir doesn't stick.
Normally cold and wet is bad. But now that Bob is the age and size he is I open his doggie door every morning and he is free to come and go as he pleases. He goes out into the cold rain or ice and snow, and when he starts to get too cold he goes back inside. Bob is a mature intelligent being and I trust his judgement to know what is best for himself. He goes out into the ice and snow and tries to find grass or weeds and when he starts to get cold he goes back inside and gets under his basking light. He doesn't get sick, knock on wood. So I think it is all up to the tortoise. Would I allow my adult Hermanni to do the same thing? No, I wouldn't. Bob is over 100 pounds, that matters. I wouldn't allow a small tortoise to do the same thing as Big Bob...