I use a pet-safe ice melter, there are many brands available and I've never had any problems. They look like little styro-foam beads and are different than old fashioned rock salt. These ice melters won't hurt plants growing nearby either.
or.....you can use sand or kitty litter, it will help with traction but these won't melt the snow.
Musher's Secret works well. When I've used it I put it on about every other day for a week and once or twice a week thereafter. I apply it before bedtime also. It's amazing how it rejuvenates the pads, makes them like new again and takes the roughness completely away. My dogs seem to like MS and one of them falls asleep while I apply it. It's non-staining too.
I would attempt coating the pads of the paws with BagBalm. It's a thick, petroleum plus based substance sold in a green can dispenser. You can get it in pet or drug stores.
I would use it before and after a walk. Remove what was used for the walk, then re-coat with a thin, fresh, clean coating of Bag-Balm. http://bagbalm.com