Tire Storage - exposed to winter elements?

[Bouchedag84]

Hey guys,
I live in Canada and it can get pretty damn cold here.
I have a set of winter tires/rims (usually on from Oct/November until May or June) and then summer tires/rims the rest of the year. Currently, my winter set is on and my summer set is in the garage and kept decently warm. I am moving next week to a place that doesn't have a garage, we just have a small wooden storage shed in the backyard that is large enough to store my tires/rims in. Should I be concerned at all about having my summer set stored in this shed and exposed to the elements during our rough, cold winters? Should I speak to my girlfriend and see if we can store my summers indoors during winter and my winters outside in the shed during summer?
We don't have heaps of room