I have been noticing that when I buy horses, the background that the previous owner had on the horse comes with the horse. I have to change it to the one I use. Assuming this is a bug because it never used to happen c:

I don't think that is a bug.

It doesn't make any sense though?

I think what Twin means is that if you have your account setting so that the background is the same on all your horses, the horses you buy should automatically convert to that/did in the past for them.

So I just bought this mare with this background:

And it automatically converted to the one I have set for my stable, so now she looks like this:

Twin, did you maybe change your settings? They should be under Account.

If you buy a horse with a default background, it doesn't stick because a default background is set for the stable. If you buy a horse with it having it individually set then it sticks because it's set for the horse.