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Having grown up up north, I can tell you that when it’s gets below freezing the humidity in the air will turn into “frost” on things…including your press and dies.

The unpainted part of your press and your dies are unprotected and delicate when it comes to moisture, so it doesn’t take much to get some rust started.

I would say your only problem is that it got below freezing, nothing else is wrong.
I would keep those things in a warmer environment when it’s going to be freezing. It only takes one freeze to frost things and get them started.

I'm sure there is a much better scientific explanation, that's just my experience.