It's not considered posh here (I don't personally like that term)
We do live near a lot of farms and rural land so there are many horse riding schools so perhaps more accessible than other places. My youngest dd is going to start riding soon as there is a fantastic place near us that helps disabled children ride, that did have a long waiting list and more expensive than other places but it's easy to see why.
As with any hobby, the costs can vastly increase from when you start. It stops being a hobby when you progress to being a serious competitor I think.
My dd started gymnastics as a hobby, wasn't too expensive to start with but now she is 10.5 and it is very, very expensive.
She is in the gym 6 days a week, everything costs! From monthly fees, physio, normal gym clothes, competition gym clothes, club uniform, country uniform for walk ons, leotards, competition leotards (different for pair and individual tumbling) weights, blocks & other equipment, competition entry fees and the list goes on and on.
Travelling is the killer, originally the competitions started locally, then across Britain and now throughout Europe with different travel for certain training too, even with sponsors and fundraising it's a lot.
So, I think skills and money can progress within any hobby or sport. My friends son was an amazing swimmer and her costs were very similar to ours now.
My dh's hobby is more expensive than I even care to think about tbh (music based) though that's more to do with the things he wants, not the things he needs! (he'd argue that he does need them of course
)