Here is another GSP cool weather exercise Idea. Buy a doggy Back Pack. Put water filled bottles on each side as many as the dog is comfortable carrying.  Then go on your leash walks as usual. I don't do this in hot weather so mainly in the Fall , Spring or mild Winter weather.

Talking to some greyhound owners in the area (eastern Ontario), they suggested the coats at Chilly Dogs (http://www.chillydogs.ca/) which keep their skinny dogs warm during the cold winter months.