Cold items brought into a warm, humid area, will suffer condensation. That's not good for powder, primers, and ammo (and guns)
I ran into this, when I converted two downstairs wood burning fireplaces, to unvented gas logs. My upstairs gun/reloading room suffered some major moisture condensation problems.
Some completed ammo, standing in reloading trays, was ruined, and had to be thrown out (in a handy lake). Boxed ammo did not suffer this fate.
It is, however, unlikely you would have high humidity (except when you do dumb things like I did) in a heated winter home environment.