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.
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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.
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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.