I tried submitting a bug report on the main page but I can't seem to find the "Create New Report" button even after I signed up. Might be a conflict with my browser or something. So, I'll look into it but in the mean time, I thought I'd mention it here for anyone to maybe tell me if it's something they've encountered also.
So, the problem is I buy a horse and then I change the saddle, let's say to the Dark Brotherhood saddle. Then I fast travel. My horse's saddle has reverted to the vanilla saddle. Save the game. Reload the save. My horse has the Dark Brotherhood saddle. Fast Travel, and now I have the vanilla saddle again. As the USSEP was the latest mod I'd installed, I curiously removed it and tested. Sure enough, the Dark Brotherhood saddle remains as it should on fast travel, so it very much seems that it's a conflict between Wild Horses and USSEP.
EDIT: AH I just found that there is a Creation Club specific patch for the USSEP, so I will check if that resolves the issue, if it does not then I will make another edit here, if I do not edit it back, assume it's fixed