Are stainless steel garage cabinets suitable for unheated garage?
Rust is only really a concern if there is water or very high humidity. Temperature doesn't have anything to do with it. In fact the Northeast gets quite dry during the winter so you should have no problems (assuming the garage does not leak).

Proper care of your tools will help prevent rust. E.g. for hand tools you can give them a quick wipe with tool oil now and then, and remove any surface rust if it appears.

A stainless steel cabinet should be resistant to rust anyway, although different grades of stainless steel are better about that than others.