Foundation design for a small cabin
Sand (as opposed to larger material with larger pore spaces - e.g. rubble trench foundation, train track ballast rock) will hold enough water to freeze and move.

If your cabin has no plumbing or electrical going into the ground, I have several 8x12 sheds supported by pressure treated lumber piers that are simply set on the surface of the ground (removing the leaves/humus, but not otherwise "digging") which have been fine for 20 years now in a cold climate.

If you do have plumbing or electrical going into the ground, movement can be a problem. Cheap foundation option is basically to go "pole building" style and set treated posts into the ground below frost depth in postholes - they don't need to be concrete piers, but they do need to be below frostline.