Yep. After the owner freezes and starts to smell bad, the dog heads back to town.
Yes, I remember reading it and it really hit me back when I was a kiddo. I think the dog sensed death, moved on and we realized the gravity of the situation.
I did a quick look around the internets, and I see there is another version with a happy ending. I don’t know which one is best; I would have forgotten the happier one a lot, lot sooner.