You can think of it this way. Your dog itself doesn't really stink like a dog when it is dry. Get your dog wet and it smells like awet dog.
I think of the dog smelling birds in the same way. If it is drythe dogdoesn'tsmell the birds as well. When there is moisture on the ground andthebirds arenesting init, it leaves a sent much easier.
You also have to be careful of dust pnemonia that the dogs can get from being in too much dust. On really dry days we usually only run our dogs in the morning when there is dew in the grass.