I do this all the time (much to Mr G's consternation). My reason is because I am chilly, but know I will be taking the coat off shortly, ie between house and car (or in Melania's case, between limo or helicopter and White House ). Or, I am chilly in a restaurant, and don't really want to eat with my coat on. It is also an easier way to carry it when you know you will need it later, but it is not quite cold enough to wear now. Final reason..... coats can really mess with the sleeves on your blouse, dragging them up to your elbows, and trying to get them down where they belong is a pain.
Some very good reasons to not put your arms in the sleeves of your coat.
And here I thought it was a fashion statement.😁
I would constantly be picking it up from the floor if I wore my coat that way.