To me, she looks more like she was stylized after a reindeer, with the shorter, less delicate legs, the longer tail and even in the shape of the horns. See how the hooves do come forward more than on a North American deer?
Also, yes. That is a small child on a full grown Mongolian Reindeer.
And while the reindeer doesn't have hairy hooves, the rest of it is pretty furry, so I could totally see taking artistic lisence to show that furriness on the hooves instead of the chest region.