After every bath I give my girls I always put moisturizer (that I use on myself) on their pads and tummys because I know how dry my skin gets in the winter. I'v never had your problem though.
Also during the winter my girls won't wear shoes, so when we go for walks outside I put this wax/cream that I bought on their pads before going out and it protects their pads from the cold and salt.
I didn't realize that that could happen to dogs. I thought their pads were just always naturally tough. I guess you learn a new thing every day!
Hope you find something that works
