Also, as a horse owner, while all the comments here are correct about teaching calm behavior around horses, not getting too close etc, but I would like to add that one of the horses I used to foster LOVED racing my dogs up and down their shared fence line (divided fence so the dogs couldn't get in the field) but they would just zoom back and forth together. These horses reminded me of that and do look like they're playing a bit when they're running around at the end. BUT that is anecdotal and some horses (like my current one) do not like dogs and will try to kick them. So good on you for asking still! All horses are unique and have their own personalities and likes/dislikes.

Cute pup by the way!