In a slightly heated garage in the winter is no problem if there is not a source of humidity, such as a car being pulled in, thawing and dripping water.
We have an insulated garage that has been kept above freezing for the past 15 years, with lots of stuff stored in it (everything except cars). Since the heat is separate from the house, there is no humidity so it is a great, cool, dry place to store stuff.
Cold air coming in during the winter will not condense on warm surfaces, it is the other way around, with warm humid air condensing on cold surfaces.
If primers become damp (not wet) they will be fine when they dry out. Primers are made from a wet paste, formed and put into the primer cups, and become sensitive when they dry.