[deekster_caddy]

Snow/Ice buildup inside the rims will absolutely cause an out-of-balance situation and is most likely what you are feeling based on the speed you described. If you have an enclosed car wash nearby that would probably take care of it. (make sure it dries good so the doors don't freeze shut, etc)

If you do go into the rim with an ice scraper (easy access, lots of room there) be careful not to pop the stick-on weights off.