If you have a baffel inside the mattress it kills the internal convection cell. Yes the matress still insulates but not as good as one where the air inside can't move. Ideally you would have a self inflating closed cell mattres, but it is kind of hard to inflate closed cell foam...though some may try.
Generaly heat does transfer up like you say, however that is because normaly heat decreases as one moves up. In the case of someone sleeping on snow the heat will move away from the source(read the heat will move away from the body) therefore in this case the heat does move downward.
Not really. Heat moves away from the source by radiation and by conduction; heat does not move downward by convection. Radiation transfer is fairly minimal (would be better if the inside of the air mattress was reflective and worse if it was black) and the air doesn't conduct heat well. Adding foam, down, or whatever may make the air mattress more comfortable and may help eliminate thin spots (that can be cold spots), but it won't improve the insulating qualities of the air mattress.