Dogs exhibit paw-chewing behaviors for a variety of reasons, often including health reasons that need to be addressed for their well-being. Paw chewing, especially chronic chewing with no recognizable cause, should be investigated and discussed with a veterinarian.
A dog that walks in snow, sleet or ice may have slush melt beneath its feet and then harden around the paws. Long-haired breeds may have more trouble than short-haired varieties, because they have more hair to house trapped snow.
Chewing on the paw may indicate that your dog has visitors--fleas and other small insects may be picked up while dogs roam outside. The chewing may be the dog's attempt to catch and rid itself of the invader.
Tending to an injury or wound may be the reason behind a dog's attention to a paw. Check the area for any sign of broken skin, infection or a foreign body that may be lodged there.
Inhaled allergens may cause a reaction in dogs that presents itself through chewing on the paws. Watch for signs, such as seasonal trouble, that may point to an allergen as a cause.
A dog that is bored, confined or stressed may develop bizarre coping habits, such as chewing. Verify that your dog has adequate stimulation, and watch for signs of other odd behavior.