>"Also, the primary function of dog booties is to protect their feet from abrasion, not necessarily to keep them "warm"."
Yes. Booties are for abrasion. Dogs can only take so much running on gravel roads (a few to maybe as much as much 10 miles) early in the dog sledding season if the snow hasn't fallen yet. In good snow conditions healthy, well-conditioned dogs run over 100 miles a day, day after day.
But the other reason to bootie dogs is to prevent icing between their toes. Much as if you had a pebble between your toes, it hurts and injures them. The musher ideally notices those conditions early and booties up the dogs (as many as 64 booties!) Otherwise, the musher has to clear the ice from each foot of each dog and then bootie them.
REI and your pet store sell a set of four, spiffy, logo'ed dog booties for $10 to $90 (!!!). Up here, everyone pays a dollar each and they are a simple pouch of nylon with velcro closure made a local sewer. If you have more than one dog and are clever, you'll get them color-coded for size.