How much horsepower?

I would guess at least 75 or 80, but more probably wouldn't hurt. I have never had too much power. It would also depend on what you are cutting and how steep your ground is. I would guess you could find on the internet somewhere the manufacturers recommendation. You will also need a tractor with dual hydraulic remotes.
I am looking at a Woods catalog and their standard 15 ft. mower that cuts 2.5 inch brush has a tractor range 45-160 hp. A Heavy duty that cuts 3.5 brush is rated at 55-235 hp. And their extreme duty that cuts 4 inch brush is rated for 65-250 hp. But they also have a 15 ft. low horse power for 40-90 hp. Tractors and that is rated for 1.5 inch brush. So I guess it depends on what you want to cut.
I have a Kubota M7040 which is close to 70HP and had a dealer that wouldn't sell me a 15' batwing, told me I didn't have enough tractor for it. Just food for thought.