Some Suggestions to keep your valueables dry with self storage:
1) Shovel snow in front of units left after plowing, snow left can create a dam where melting snow from roof hits and causes water to run backwards
2) Use pallets to elevate any items that cannot get wet, cardboard boxes are not good at keeping your items dry, in fact they can pull moisture from concrete and get your possessions wet.
Unless your units are climate controlled this is a common occurrence with any outdoor storage facility. Any operating outdoor facility saying this isn't a problem is lying, this happens everywhere there is snow.