These days, the officer would probably wear dress blues (not the mess one, but the one that looks like a regular jacket) and black boots. Fort Leavenworth is the only remaining military hunt, and it’s rare to see an officer in uniform, but does happen now and again. I have seen soldiers in uniform hunting at both FLH and Artillery over the years, and the color guard from Riley did hunt in uniform at an FLH opening hunt several years ago.
One problem is that I’ve never seen anyone wear a helmet with dress uniform, it’s always a service cap.
I’ve seen one guy show up in a historic cavalry uniform, more a reinactment outfit and not true military dress. That probably wouldn’t be acceptable most places.
Traditionally, proper military uniform is always acceptable (it used to be a requirement for calvalry officers to either hunt, play polo, or event). But as far as your particular hunt is concerned, there is no point in speculating, ask your MFH.