My husky mix has the same problem. I always keep the fur cut short just like your pic. It not only keeps it cleaner but helps a lot more w/ traction. In the snow it actually helps to keep them short so the snow does not clump on on the hairs and can cause frostbite. I keep a "mudday paw towel" in a bucket near the door & wipe them everytime he comes in. It does the job & easier than washing them everytime.