I would agree that sleeping on an air matress with inadequate insulation in the winter would be chilly to say the least. It is difficult to impossible to warm up that volume of air with your body heat to the point that you would feel comfortable. However, laying directly on snow would be much colder.

I remember in my youth, sleeping on the ground in the winter in what today would be considered at best a 40 degree bag (and shivering all night!!). I can't do that anymore with my back. When I don't travel far from the car I use a 6" inflatable Colman matress. When backpacking, I use a 1.5" Thermorest. I try to match my sleeping bag to the weather, then the air matress is mostly for comfort plus a heat transfer barrier. Dead air space is always better than putting a sleeping bag directly on snow in my book.