I'm from northern Minnesota and this type of construction, especially for residential, is becoming very common for structural slabs on grade. Frost depth here is 5-6 feet deep and it usually becomes much cheaper than excavating for full depth footings if a full depth basement is not desired.
As dik mentioned, the earth provides heat, a constant temp of 50 deg F - always. For an area such as here, this can mean a differential temp as much as 100 deg F compared to the outside temp. It is therefore important to provide a means of stopping frost penetration into the foundation area. Keep in mind, frost mainly travels downward - not horizontally.
Generally, I use 2-3 inch thick(2-3 layers 1 inch thick, lapped) type 4 extruded polyethylene (R9-13.5, blue board or pink board depending on brand) along the vertical sides of the thickened slab and 4 feet out from the slab around the perimeter. This is conservative but utilizes the full sheet of insulation board-usually in sizes of 4ftx8ft.
Some items to remember:
Make sure the structure is heated and insulated BEFORE freezing temps have ocurred.
Provide drainage as dik also mentioned. This is important since heat is conducted thru moisture much faster and can subsequently freeze.
If the vertical insulation above grade remains exposed, it must be covered with a protective coating against UV damage.
I have also used this concept in designing "frost-free" footings for columns ,piers, and walls by pouring directly on the insulation under the footing.
A good guide to use is in the 2000 IBC for residential construction. (Starting at R403.3). There is also a free energy program called MNcheck.