I'm not enjoying having a standard horse again after my Pestilence met an unfortunate end,so I was thinking if there's a way to perhaps buy horses like in the original game?

Well there are 3 other undead horses still out there.
 
War outside Bonnie's Rance and in other places. Famine is in Mexico somewhere.  Then you can get Death at the end of the game or after getting the other 3. 
 
After that and you do all the horse challenges you get blood pacts for each apocalypse horse that works just like the horse licenses did.

Once you get the final horse, Death, you have to run over each type of undead in order to buy a deed of the four horses
 
I don't know if you can actually get death after the story is completed but for me as for what I assume for others, I did not get the final horse until after the main story