Maybe consider just adding in the mount ability to all classes and put in various stables where they can be procured. Grinning skulls could have the warg den (maybe Pine forest has a dire wolf tamer for you), some unholy place allows the nightmare to be summoned, etc..
The thing with the mount would be to make them restrictive in some manner such that not every PC is using them. But there would be a niche perk to them regarding mobility.

And make the mounts mostly frail (maybe they are like mercs, where they cap out at like level 30) and ineffective melee group mates (in most cases at least) and make it so fighting is fairly limited while mounted.

Make dismounting quick/easy, put some lag on mounting so it has a risk to doing it as an escape mechanism.