Hauling all of your extra things off to a storage unit can be a pretty demanding endeavor, especially if you have large furniture or appliances to put in there. As such, it's probably an endeavor you want to schedule. But what if your scheduled storage unit move-in day arrives, and the white stuff is falling from the sky? If there are travel advisories or you feel unsafe, you should probably reschedule, but for the average snowfall, there's no harm in pressing on—so long as you take the precautions below.

Use moving blankets to cover items as you carry them outside.

You don't want snow to fall on your items when you are carrying them from your home to the moving truck or from your moving truck to the storage unit. Even if the items themselves are not moisture-sensitive, if they are damp when you put them into storage, they will introduce moisture to the air, and that will make things mold. 

Keep a large stack of blankets on hand for this purpose. When one starts to get damp, set it aside and switch to another one.

Put absorbent rugs down on the storage unit floor as you load it.

When you arrive to the storage unit with your things, take a few minutes to put mats down. These should be mats with a rubber, waterproof back, but with an absorbent, cloth top. The idea is that the mats will absorb any wetness and salt from your boots, so you don't have to take your boots off every time you step into the storage unit. 

You may have to shuffle the mats around a little as you create piles of boxes and as you situate various things in storage. When you're done loading the unit, pick them up and take them with you. Do not leave them behind; the moisture they contain may perpetuate molding.

Put some silicone desiccant boxes in the storage unit. 

Buy a couple of boxes of silicone desiccant—the kind people use to dry out basements. Put them throughout the storage unit. This way, if some of your things did get a little moist with snow, or if you did dampen the floor with your boots a little, the desiccant will at least absorb some of the moisture from the air to reduce the risk of molding.

Snow should not keep you from loading your storage unit, in most cases. Just take the precautions above, and go for it!