Best companion for an equine is another equine - they're a herd animal and although some will settle for another species, others will not and if you're going to invest then you may or may not be lucky about the individual compatibility aswell as the general suitability of the species.
Donkeys carry lungworm which can affect horses, they are also not low maintenance, despite how many people keep them and as another poster says, they're desert animals not well suited to the climate here so will need good shelter and careful monitoring.
Can't talk about goats as I've never had them. I have had sheep and cattle in with ponies at various points, lambs are too vulnerable to ponies chasing them for fun, cattle tend to chew tails for some reason, not to mention being higher maintenance again and probably too big for your limited grazing. I had tups summering with ponies from March to September for several years and they stood up for themselves and all got on fine, but it also helped a local sheep farmer and got me access to stubble and winter grazing as a return favour.
I wouldn't keep a sole equine though personally - if you really have limited grazing then a small pony or two would be best by far - in my opinion - for your horse. Two if the one you get won't be happy being left behind while you ride unless you want to ride and lead every time or come back wondering if the pony is sweated up, colicking or has escaped to chase after you! Ponies are dirt cheap right now if you don't need any particular ridden experience - shetlands are often given away as companions, there's one at the farm where I just sold a pony to and she's a mini 6yo mare - doing a good job keeping the new boy happy until he integrates but after that who knows..