[Yeaaah she couldn't really tell from the glance she had at the dog before what she was working with exactly. Easier to just cover all the bases.]

I'd say since the dog is still hanging around, even through the cold? That's a pretty big sign it's happy to stay with you. Why not ask it and see what it thinks just to make sure?

[If Korwa knows dogs, say anything to them in a happy voice and they'll be all wagging, all panting, 100% excited. They might have no idea what you're saying but that's fine, it's the reaction that's important.]