The field is going to grow X amount of hay, whether you let them eat it as it grows or cut and bale it, your production will be about the same. Using it for hay will incur the additional expense of harvesting.
More cost effective to let em eat it in place.
Sayign that. 4 acres is gonn aget mowed down pretty good by 2 horses, 4 will over graze it. Id also look into zoning laws. Many places are putting acreage and setback limits on horses. If I knew I wanted to keep 2-4 horses I wouldnt even consider less than 10 acres of grass. NOT buying hay all year is a big money saver.