I trim the hair between Graham's toes weekly, otherwise he also gets snow clumps and he tries to frantically lick the snow out of his feet because it huts. I would start with clipping the fur off the bottom of the feet at least. It sounds like that pup might benefit from a haircut all around (not too short, so it won't get cold, but short enough to prevent so much snow buildup). I also recentally bought dog booties from a company called "muttluks" http://www.muttluks.com/

They have socks attached that go up the leg and they are pretty comfey to the dog (he likes them better the the Fido Fleece booties I bought him) and they absolutely do not fall off. They keep the snow off and they also prevent the pups from stepping in that painful salt.

So a haircut at least on the bottoms of the dogs foot, preventing snow build up, a possible full body clip, and good set of comfortable dog booties.