Is cornering in snow any different? The general advice about cornering is to lean the bike, not the body, to put pressure on the outside foot, and not to brake or brake only with the rear brake if absolutely needed.

Well, does this advice hold for snowy terrain? 

Today is my second day riding in snow this winter and still have the feeling that if I lean the bike, it will simply slide out under me. The tires are Schwalbe Land Cruiser. So I actually lean my body, keeping the bike as straight as possible through the turns. Exactly opposite to the general advice.

I am talking about 10km/h riding, and I already managed to fall a couple of times (luckily at those speeds falls are harmless, when outside traffic).

"On snow" for the purpose of this answer means autumn leaves, over which there are several cm of frozen, hard or melting snow.

I am fortunate that 1/3 of my commute is through a non-paved park, where I can practice funny things without the danger of being hit by a car. There are even some small (30cm) and other not so small ramps, but I haven't summoned the courage to jump those ... yet.
It's different insofar as walking on ice is different from walking on concrete. Traction is reduced anywhere from somewhat to greatly. It takes a much smaller change in direction, much smaller amount of braking, and much shallower lean angle in a turn to cause you to break traction. In terms of the physics and techniques involved, they're the same, though mountain bike techniques come in handy as you are likely to spend much more of your time without traction compared to typical riding on paved surfaces.