So much depends upon the quality of the ground.
Is it on the flat or does it slope?
How long has it been used for horses?
What is your method of husbandry?
What is the climate like all year round?
There can be no hard and fast rules.
In the UK we can take 1 -1.5 acres per horse providing the field is flat and the sub surface relatively hard and horses have not turned the field sour.
But good management means that the field must be kept free of dung by collection and that the field should be divided up with electrified tape, especially in the grass growing season. In the UK one also has to watch for toxic weeds.
Then there is also the question of whether the horse has a stable to sleep in.
Field shelters, even a small copse of leafy trees can be utilised for shelter but
Nothing replaces a loosebox type of stable - of minimum size 12ft x 12ft.
Most continental Europeans keep their sports horses permanently in stables and let them out for a few hours each day. The horse's diet is carefully controlled and the role of the field is for relaxation and not for feeding.
I would never rely on paddock grass alone for feeding - it is not a constant source of food - in the Spring there is too much; in the winter too little. In the Summer it is too green and fresh; after a frost it is too sugary. It may lack in minerals such as magnesium. The owner has no control over calorie intake and cannot provide a balanced and constant diet. For humans we say "we are what we eat" - that saying applies to horses as well. A horse's behaviour is strongly influenced by its diet.
In the old days, in cities they kept horses divided by swinging bars in stables.
The horses were tied to the wall by the head. The British Cavalry - especially the Horse Guards used this system to manage their magnificent horses until relatively recently. Go visit the stables in London.
Horses were "stalled". The horses went off once a year to camp out in the country where they were allowed access to grass. Feeding was a separate issue. The horses would have been fed 3 or 4 times a day with selected feed stuffs including very carefully chosen hay. Hay varies in calorific value - some hays can even be toxic if they contain weeds such as cut ragwort. Musty or dusty hay can give chest problems.
I have taken the decision that my horse's field is primarily to give her exercise and stimulation. I feed her regardless - it is just that at some times in the year she gets more bulk but fewer calories. She is fed according to work load and temperature. The belly tape and my eye always tells me when she's eating too much. She is restricted at the moment because the new 2010 sugar rich grass is coming through and that could induce laminitis. Anyway she has run around the field, which is currently too wet and has churned it up with her steel shod feet. The third of the one acre hillside field which she is not normally allowed access to looks good but she can't have access to it. The huzzy has twice broken through the electric fence divider. That retained area will be released to her in March - in narrow strips but she'll lose each day as much area as she gains each day.
If I had access to it, then I would keep DiDi, a silky Irish Draught with Thorobred blood in her veins, in an undivided big barn, surfaced by wood chips and absorbent wood power. She'd live along with other carefully selected mares with whom she did not fight. She'd be extracted from the barn to be fed night and morning. She'd sleep overnight in her own loose box. She'd only be let out on the pasture with other horses when the field was dry and the sun was shining. She'd always wear a lightweight rug with a hood to keep her dry and clean. She'd be kept away from all geldings when in season. As I have written in another thread - I would be her jailer if I had the facilities.
If I still had Joe, a tough hairy cob gelding, I'd leave him out in a field in which was a substantial wood field shelter - affording shelter from the rain and wind from whichever direction it blew - together with a companion horse or pony.
Either the field shelter would be mobile or I'd pay especial attention to the location and the composition of the floor of any fixed shelter. He'd be left unclipped. He'd be given nightly one substantial meal of pasture mix and additives. If the grass got too poached or wet then I'd leave him with hay, loose on the ground. But unkempt Joe was used to living out on a hillside.
Collection of the dung is important - it should be left to convert to compost and taken away regularly by a farmer. In the UK the management of any commercial compost heap is subject to local inspection. Uncollected dung sours any field and provides a habitat for worms, flies and bots. Horses won't eat grass which has been staled by dung or urine. It is a good idea to allow sheep to graze pasture retained solely for horses. Sheep eat everything green which a horse will leave behind. Such sheep taste good.
So your question is difficult to answer - there are too many variables. First decide on your system of husbandry based on the facilities available to you. But lose the idea you can leave the horse out in the field to fend and feed for himself - they don't make them like that these days. You guys however do still have mustangs - I'm told they fend for themselves. Bliss.
But welcome to the horse owners club. This subject ain't easy to get right.