By all means check your LOCAL zoning laws first.
When I lived in NW PA the zoning laws varied from township to township, but for the most part in my county the minimum acreage for any sort of livestock (including goats or sheep) was five acres.
Growing up, five acres per piece of livestock was the Rule of Thumb. Now that I am retired and living south of the Mason-Dixon, I called my Ag Guy to see if things have changed. His reply was five acres per piece of livestock is still the healthy Rule of Thumb; anything less and the Owner really needs to learn how to micro-manage the land to keep the horse healthy.
You could almost be asking for trouble to put a horse and even a small companion on one acre.
There are books that tell how to manage a horse on small acreage; I have seen them in Tractor Supply and if you Google "managing horses on small acreage", I'm sure you will get a few hits.
One thing you have to be prepared to do is to hay the horse 365 days/yr. One acre of grass might
last a month and then he's down to eating dirt.