It's odd the way some do grow winter coats and some don't. An Arab mare I had, straight Egyptian and only second generation from an import grew so thick a coat she looked almost like a mustang. Two of my app mares have very thin coats and appaloosas started out as mustangs more or less. I guess it could be crosses to Thoroughbred back in their lines but it doesn't seem to run in a particular line at all.
Okie gets long hair. Sarah Lee just gets a thick short coat. You don't notice until you brush it out.