With google its quite trivial to get actual data rather than estimates.
It doesn't seem controversial that per IIHS stats motorcycles have about 30 times more fatalities per 100K miles than cars.
Likewise I have no reason to disagree with an online Br J Sp Med journal article from '91 that horse riders experience significant accidents once every 350 hours whereas motorcyclists have a serious accident every 7000 hours, or about 20 times more risky, based on ER reports.
So multiplying risk, it seems horse riding is about 600 times more dangerous than passenger car driving.
Another interesting anecdote is "everyone knows" that most accidents happen to noobs because they're distracted so much by learning and not knowing their limitations. So what you're really measuring is the fraction of low time noobs who will be injured by the sport before they escape noob status. That hypothesis would predict that essentially all horse riders will be injured in some way before they escape noob status, a noticeable fraction of motorcycle riders will be injured as noobs although the vast majority will not be injured, and its actually VERY rare for a noob car driver to be injured while learning to drive. In summary, this seems to be a situation where perceived risk matches actual risk.
It would seem as a civilization we do an adequate job preparing teen car drivers as the vast majority of drivers survive their teen driver years, but as a civilization we do a completely inadequate job training horse riders. Or at least based on British data from the 80s as reported thirty years ago; I'm old enough to remember nobody wore bicycle helmets before the 90s; perhaps modern horse rider trainees wear better safety equipment in 2020 than in 1990.
Strange start up tech idea: Smart helmet with GPS and machine vision for horse riders with AI and machine learning to yell in their ear when they're doing something dumb. If essentially all horse riders are injured while learning, they would likely be very motivated to drop some money on your smart AI safety helmet. On the other hand actual risk data indicates a similar product for teen drivers simply wouldn't sell, not having the proposed theoretical magic helm already has a very low accident rate making the helm appear less useful. Edited to note: that's the entire point of my risk rant, do a startup on fixing a problem virtually all of the customers have, not a startup on a problem essentially none of the customers have.