What is the ruling on walking over dog footprints in wet snow, and is it permissible for them to touch clothes?

Scholars have differed on the impurity of dogs, holding three opinions: complete purity (Maliki school), impurity of the dog and its hair (Shafi'i and Hanbali schools), and impurity of its saliva only with the purity of its hair (Abu Hanifa's school, a narration from Ahmad, and the choice of Ibn Taymiyyah).

Shaykh al-Islam argued for the purity of dog hair by stating that the default for things is purity, and that the hadiths only mentioned the impurity of the licking (walūgh). He also argued that claiming the impurity of its hair would cause hardship and difficulty, as Islamic law permits keeping dogs for guarding and hunting. Based on this, there is no harm in walking on dog paw prints, and neither footwear nor clothes become impure by it.