When you excavate your footings you will need to reach below the frost line depths.  This is the depth at which the moisture present in the soil is expected to freeze.  Once your footings are buried below the frost line the ground will act as a barrier to insulate the soil below the footing from freezing in the winter. 

The depth you are required to set your frost footings will vary from region to region across the country. In very cold regions like ours (New England) you will need to dig down 48 inches (4 ft).  Always check with your local building inspections department to see what is required in your area.