Same situation but I park in the garage. I haven't noticed any issues with my reloads. I put the powder back in the original containers when done for the "season" and make sure they are closed tight.
Probably better to have them in the toolbox rather than bring them back into the house. The condensation (cold garage to warm house) would be trapped inside the container with the primers.
It's fine. Worries about condensation are baseless. The primer compound can get wet and be dried back out and be the exact same. The compound is designed to get wet and dry out fine, because that's how it's handled in the factory during assembly of the primer. Loading primer cups with dry compound would be rather dangerous.
Same deal at my old house. I stored dies, powder, and primers in the house. Warmed up the garage for a loading session. Only bring out what I'm going to load. Once ammo was loaded it goes back into the house. Also spray down press to prevent rust.