What you're experiencing is called an ice lens. The soil freezes and attaches itself to the foundation surface, so when it heaves it takes the foundation up with it. It can occur with all foundation types in areas that have frost in the soil, even poured foundations can be lifted off their footings. In the old days architects specified visqueen plastic be draped along the outside of the foundation wall before backfilling, it acted as a sliding lubricant to keep the frozen soil from attaching to the foundation and lifting it up. These days it's so common to have sub grade insulation on foundation walls that the insulation plays that role. In your case you could do a couple of things, the simplest being to wrap the posts with visqueen and then backfilling again.
The devices designed to prevent uplift (cleats nailed to the bottom of the posts, rebar through the post, etc) are intended to prevent uplift caused by high winds. They can't resist uplift due to frost because the forces involved are too large (see below).
The skirt boards may be exerting an uplift on the posts due to frozen ground under the boards, but the fasteners would fail before they actually lifted the building. In your area the snow load is probably 40psf, so for your building just the weight of the snow is 40x60x135= 324,000 pounds. If you have a hay loft you can probably double that number. The weight of building is probably another 10-20psf depending on construction style. So you're looking at a minimum 500,000 pounds spread over however many posts you have. In a building that size I'm guessing you have three dozen or so load bearing posts, so each one is carrying 500,000/36 = ~14,000 pounds. No fastener is going to withstand lifting that amount of weight, and no uplift device is going to keep it on the pad. If you did anchor the post firmly to the pad, all you'd succeed in doing is lifting the pad up. You need to make sure the soil can heave independently of the foundation elements.