Op beech/hawthorn mix would work or even gorse if you are prepared to not let it get out of hand-I know some people hate the stuff but I love some gorse in a horse paddock personally-they can safely eat it and it’s hardy as heck.
It's not always easy to tell if a certain tree or plant is toxic for horses. There are plenty of lists out there, but many seem to be incomplete, and sometimes there is uncertainty as to the toxicity of certain species. In any case, I doubt you'll find many fast-growing non-toxic native evergreen.
How high do you need these trees to be, and how quickly can you wait for them to reach that height?
If five or six feet would do, it is more like a bush or hedge, to me.
Hornbeam or beech might get that high in about three to five years. Hawthorn and gorse maybe a bit quicker.
Poplars are lovely and very good all year round as a windbreak. I thought beech nuts were poisonous for horses? We have a beech hedge at the RDA that I sourced, but it is fenced off so the horses can't get to it.
Having had the vet out for blackthorn vs horse's eyelid and having to go to hospital for blackthorn in my hand (it can cause very nasty infections in humans too) I would never choose to have it in a field. It also suckers underground like crazy and rapidly gets out of control.
It looks more messy but I'd go for a mix of bramble, dog rose, hazel, hawthorn and pop in some willow, birch and poplar into a row. And fence it off for the first few years so the beggars don't eat it straightaway.
The only thing might be, if your place is very exposed, is that the soil is already quite dry where you want to plant - you might need to water if we have another summer like last year's, just till the plants establish.
Mine will also munch on dead fir trees if given a chance, and my friend's Fell will eat fir too while out on a hack.