Are you in the US by chance?
It looks like Sony US has not enabled the DLC yet.
This thread was added on December 05, 2019, with posts from Tascha.
Thanks!
looking into it.
It’s the same as with other DLC pet skins: You get special food you feed the horse (it’s a feat) 
Regarding the DLC:
We have contacted Sony so they can look into it.
More news as we hear back from them!
Yes, however that is most probably a different issue. Most steam users forget that they need to restart steam for the update to be properly recognized.
We just tested locally here and steam seems to work fine. (I will still keep an eye out for any answer or additional reports for steam DLC issues).
Also, keep it civil please. Remember language and undertones/sarcasm. Yeah?
Thanks everyone <3
I mentioned above that we are working with Sony on this. It is an issue in their side.