I think Cecil missed out a whole aspect to the dogs getting frostbitten feet thing. From my experience (and I grew up in the Yukon, where dogsledding is considered a perfectly legitimate and popular sport) frostbite is not a problem because before a dog gets frostbite, it will get balls of ice building up between its toes. These balls of ice are understandably uncomfortable (try walking around with ice cubes between your toes and see how you like it) and the dog tries to chew them out. Because dogs lack sensitivity on their feet anyway, and because their feet by this time are probably additionally numb with cold, they often miss when they’re chewing out the balls of ice and puncture the pads on their feet with their teeth. This makes them bleed and hurt, and if they’re on their own, they just curl up somewhere and lick their paws until they’re all better, or if they’re attached to a sled team, the musher usually notes the blood and pulls the dog. THIS is the reason why dog mushers put their dogs in booties (the material of choice is the same polar fleece that ski pullovers are made of) and quite a few people up north actually make a decent living selling fleecy little dog booties to mushers.
Anyway, that’s just my input. The answer I think Cecil was going for was “They are capable of getting frostbite, but other injuries usually occur first.”