There are hakama made specifically for riding horses so he may have been wearing that style. It’s called umanori hakama which means horse + riding/up on hakama.
Hmmmm, I’m thinking he should try riding his dressage test in hakama - that would be a sight to see!
Though it looks rather voluminous, it’s meant to be promoting ease of movement. Here, you see men doing all kinds of traditional sports in hakama, like mounted and unmounted archery and even martial arts. Samurai wore them as foot soldiers so they must be reasonably easy to walk and run in.
I’ll sometimes see men in hakama on the metro with their traditional bows in carrying cases, which is kind of cool. The longbows are massive!
(these gents aren’t in hakama, but you can imagine one of these bows on the subway
)