If I carry my swim bag over my shoulder, it puts a strain on the shoulder joint. Holding it in my hand isn't much better. If you're wondering why my swim bag is so heavy, it's because of the added weight of my pool shoes.
When a friend offered me her son's old wheeled backpack, I gladly accepted it.
It's so much easier to wheel my swim bag from the car, into the facility and to the change room.
Fortunately, we rarely see snow out here on the West Coast, so I don't need to make a switch to "winter tires"!