Yes and YES! PA really needs to sort this out!!

They could use the mouse as a means to change the minigame. For example you could move left/right or in circles rather than crazy tapping spacebar. It's a silly mini-game that provides zero challenge to anyone who has no disability and only causes damage to spacebars lol. Poor spacebar....

Like maybe when the horse pulls his head you have to move your mouse the other way or something as you're walking towards the horse. IDK, something interesting.

Maybe holding and releasing the Mouse Button, to have it within a "green bar" similar to Wheelbarrow minigame while the player is pulling himself with the rope closer and close to the horse?

As a disabled person with severe arthritis, I would also really like it if you changed the minigame...it kills my fingers. Oh and it sucks.

 Oh this sounds like a good choice , lot better than the curent spacebar beating

Perhaps you can do it like the initial one where you press once within the good area? your training mastery/level determine how wide the "Good" zone is and/or how fast the bar moves. 

Short info for you: In the new patch this wednesday, the horse Minigame will be changed:

Major Update Details

● Horse Taming minigame will be made easier.

As this change is not on Glabs or anywhere else, we dont know what exactly it entails. But here's hoping it will now be accessible for everyone, no matter their hardware or (dis)abilities.

That is good news!

this space smashing was what broke my last keyboard

i think there is an update to the minigame comming but idk exactly the change 
just checked and yeah with maintnace 

"● Horse Taming minigame will be made easier."

hopefully it works.. i know people that physically cant do the capture part