The human body can synthesize vitamin D in the skin from cholesterol, when sun exposure is adequate. But how can haired mammals do it? Do not they need it?
According to "Melanocyte biology and skin pigmentation" (Yin and Fisher, 2007), the exposed parts of mammal bodies, such as their noses have melanocytes that can be locations of vitamin D production.
According to this Wikipedia article, the secretions in woolly animals also produce vitamin D.
This is further explored in "Vitamin D(3) synthesis in the entire skin surface of dairy cows despite hair coverage." (Hymoller and Jensen, 2010), where they found that cows synthesise vitamin D all over their body, where they dispute an idea that vitamin D is manufactured in the fur secretions, and ingested via grooming.