Sheep owner here
. They are complimentary grazers in that they don’t share parasites, eat the same high-quality hay, and do best in the same high-quality “horse” fencing of woven wire with 2x4 squares.
They have different mineral requirements and are very susceptible to parasites.
I find my sheep do not reduce my mowing time. I’d need a MUCH higher stocking rate and intensive rotation to force them to graze down problem areas. Rotating is much better for parasite management, but takes time and/or infrastructure.
Their mineral requirements are unique. You’d likely need to rig a sheep-proof place for your horses’ minerals and a horse-proof place for your sheep minerals, or rotate the sheep behind the horses. If you need to keep your sheep on the same ground year-round, you’re going to have parasite problems and will need check for and worm regularly.
I have Katahdin and don’t deal with shearing or horns. I expect hoof trims to be easy for most any horse person, as long as your back can take the bending over.
50 head on 20 acres of good grass and still mowing every few weeks during the season. They pick and choose spots just like horses, leaving poor, rough patches tall that have to be mowed before they go to seed and expand the problem areas.
I cheer when I see mine climbing up a tree to reach poison ivy!
Aside from a particular species or two of invasive or undesirable plants, they prefer good grass just like horses.
Mine have never climbed on the fence or gotten out but they have tons of good grass, high-quality hay and a hot wire over woven wire fencing.
I enjoy watching the sheep head butt, play king of the hill, and get the zoomies. That’s enough entertainment for me. I will never have goats, no matter how cute and cheap are the kids. Want to see if you have a goat-proof fence? Throw a bucket of water at it. Did water go through? So will goats. 
All that said, sheep are a low-input, affordable animal to raise for market if you enjoy them. If you want them to reduce mowing, you’ll be disappointed.