BB has answered your question. Dogs are smelling gases that come from the bacterial eating of dead skin cells that come off all living mammals, and birds. The dead skin cells are warmed by the body's heat, and the bacteria is already working on eating them when they fall off the rabbit, or whatever you are hunting. I have seen clouds of apparent " dust " from an escaping pheasant, in the air behind them as they beat their wings to climb, but most of it is not " DUST" from dirt, but simply an accumulation of deak skin cells, under the birds feathers. Its this sprinkling of dead skin along the flight path that allows dogs to follow the scent trail to the bird, after it is shot and falls from the air. Good bird dogs will circle down wind, out of training, and habit, to pick up the strongest scent trail to follow, and in a cross wind, that can be many feel downwind of the actual flight path taken by the bird.
With rabbits, their scent stays pretty close to the ground, even when they leap, and then its all over surrounding weeds, and brush, at " Nose " level for the dogs to catch on the run.
The only problems dogs have in scenting game in the snow is the cold DRY Air, makes it hard on the dog to keep his/her mucus membranes in his nose, and upper mouth wet, to flush the scent off, so he can breath in new scent to continue to follow. Its important for hunters to give their dogs a break, periodically, and give them luke-warm water to drink to replenish their fluid levels. The colder the weather, the more often dogs should be both watered and fed a little. ( As the temperature drops below zero, the air loses more and more of its moisture, to the point that unless you are exhaling moisture, you own lips can dry to the point of cracking. )
