It is not a good idea to leave a basement completely cold, as this subjects the walls to freezing. A crawl space under the house can be left cold by insulating the floor above, but less insulation is required to simply insulate the perimeter of the crawl space (although you will have higher heating bills, you are heating a larger space). Venting ducts and plumbing pipes in an uninsulated crawl space must be insulated. Remember that water pipes, even if they are insulated, will freeze if the water sits still for too long. A house on piles with no pipes underneath can be effectively insulated under the floor, although a skirt should be erected around the house to keep out the snow and the cold wind.
Warmed space means partial insulation under the floor and partial insulation on the perimeter, either for a basement or a crawl space. This keeps the space significantly cooler than the house (less heating load for the furnace) but above freezing. About sixty per cent of the insulation should be under the floor and forty per cent around the perimeter. The vapour barrier goes with the perimeter insulation -- not with the floor insulation above. You could put RSI - 3.5 (R-20) under the floor and RSI - 2.1 (R-12) on the perimeter. For much greater comfort and ease of application, use RSI - 4.9 (R-28) under the floor (it stays up by itself because it is so bulky) and RSI - 3.5 (R-20) on the perimeter. This will leave the crawl space at about 9 degrees C and keep the pipes from freezing. At the same time, it permits a small heat loss that will keep the foundations from freezing too. Where it is not practical or where you are unwilling to go to the trouble to put a moisture barrier on an exposed earth floor (search keyword "moisture barrier" for the title "WHY PUT A MOISTURE VARRIER UNDER A HOUSE?"), this cooler temperature will minimize evaporation from the soil and drop the relative humidity in the space considerably. This split insulation method is particularly recommended for crawl spaces in colder regions, especially the Prairies.
Heating the space under the house to room temperature is done when: the space is to be an active part of the house; the heat needs to be applied to the foundation to protect it from frost; or it is easier or cheaper to insulate the perimeter alone rather than both the floor and the perimeter.
All energy conservation questions aside, the floor above a heated space is always more comfortable than the floor above an unheated space, and that despite massive amounts of insulation.