We never wash our belts, although they are the first thing we touch when leaving the toilet, even before we wash our hands

You're supposed to wash winter coats?! Next you are going to tell me that you have to wash blue jeans!

I think it depends on the belt. Washing some types of belts would absolutely ruin them. But yes, people should absolutely be washing their winter coats!

I wash my coat from time to time because I consider and have considered it to be part of my wardrobe. For my belt, I suppose I kinda just considered it as an accessory and it never occurred to me to clean it.