Well, I've been storing my bikes in an unheated garage in northern Wisconsin in the winter for more than 30 years and haven't noticed any undue wear on the rubber parts. The only problems I've had were with some Panaracer road tires checking badly over one winter. I attribute it to bad tires, not the cold. Other bikes with other tires fared fine in the same conditions. Currently I store a full suspension, commuter, fixie, tandem, two road bikes and my wifes hardtail in the garage. The single speed is in the basement because I don't have wheels for it right now.
The main issue is condensation. Bringing bikes in the house when it's cold outside causes condensation. Another enemy is ozone. That's what attacks rubber. Keeping rubber away from ozone producers is a good idea. Electric motors are ozone producers.