Steel Truck Rims Should I Rotate My Tires?

Should I Rotate My Tires? - steel truck rims

Currently I have installed 4 ZIEX Falcons (low pro) at 20 "American Racing Wheels. I live in Canada and winter is approaching. I plan my winter tires and steel rims for my truck (2WD), in the coming weeks, perhaps a month or so.

Last week I took my car, threw the car wash and the loss of weight on the tires on the passenger side balance. Has the experience in the areas of brakes, the steering wheel shake at 90 km / h. I drove over 500 km in this way, and I took inventory turns, and about 15,000 km long, since I bought the car.

Does it make sense to convert the balance for me in the winter in a month and a half or two, or I'm waiting until the spring, and they even rotate and balance?

If so, I chalk the tires, which are each new tire rotation and only set in the same place in the spring? (It would still be compensated?)