the arena is small. It's a bit messy
There are work rounds and I've known people compete in showing classes at HOYS with no arena to practise in. It's not great for getting the angles right in dressage but one advantage is that when you do get out, a 20 by 40 feels quite large. So I think if everything else is right, don't worry too much about that.
As for messy, it depends on the kind of mess. I had my horse on a super tidy showing yard with very little turn out. When horses got loose they were more inclined to go a bit loopy and damage themselves, because even on a tidy yard a horse will always find something. Now he's a on a messy yard with a lot of turn out. Places he could easily damage himself, like the feed room and the tack room, are shut. There are no nails around or glass, because there are a lot of vehicles around and no-one wants a puncture. If horses do get loose they tend not to be too bothered and will often just put themselves away.
Last time my horse got loose was my fault because I parked him whilst I helped someone with a gate and he wandered off, but he ambled round any mess and found some nice grass. And I ambled after him and we mooched off to the yard together. If you're laid back, they tend to be.
So now, if I need to move yards, I'll make a list of priorities but they'll have to be his priorities, not mine. He needs year-round turn out. It doesn't have to be a huge amount, but he cannot go back to being stabled as much as he was on the posh showing yard. It has to be friendly and there has to be reasonable hacking, but I'm not insisting we get off road immediately. A school would be good, and the ability to bring in freelance instructors, but they're my priorities rather than his.