I don't think the No.1 would be any more susceptible to freezing than a bolt action, maybe less.

The number has an internal hammer that strikes the firing pin, it's not striker fired like a Dakota No.10. The hammer is held under some pretty heavy tension before release. I would think that this type of setup is less likely to freeze up than the typical bolt action.

I may be in left field on this, but I don't think the person that told you this knows what he is telling you. Even though I live and hunt here in Alaska, I have to admit, I haven't used my No.1's when it's been colder than about -40*F.