I hate to sound like a prick and rain on your parade but this is working as intended.
The buff "Festive Holiday Mount" just turns any mount that you Dismount and Remount into a reindeer, give it a go you can change all the mounts and they all shift to reindeers.
Once you mount up You gain another PASSIVE buff called "Reindeer" that does not have a timer and means your mount is a reindeer and will stay until you dismount.
I know you tried to contribute but yeah the holly just turns any mount you mount while having the buff into a reindeer but they stay a reindeer untill you dismount anyway give it a go, mount up, hit holly, right click debuff, BANG STILL MOUNTED