This is actually a fairly common problem in extremely cold climates. I lived in Wisconsin for ten years, and I saw it frequently there. You are correct in your analysis, when snow melts in the spring, and the ground is still frozen, the frozen ground acts as an impermeable layer. This causes the water to sit on top of the frozen ground, and effectively raises the water table temporarily, until the ground unfreezes, and the water can percolate downward. You don't get the problem during summer rains because the permanent water table is probably well below your basement elevation.
Solution: As previously noted, make sure the ground slopes away from your house at a minimum of 1 inch per foot, preferably 2 inches per foot. That way, when the snow melts, the water will not pool next to your house, and will be discouraged from penetrating through your foundation wall into the basement.