Horsepower is not the only thing to be concerned about. A haybine is a heavy machine. 35HP is probably the minimum needed to operate it. However, most 35HP tractors will get thrown around with all of that weight hanging off to the right side when you are operating it. My recommendation would be at least a 50HP tractor that weighs at least 7000 lbs.
My experience with a haybine is running one on my dad's farm back in the '70s. We had a New Holland 9' Haybine and pulled it with a 3020 John Deere that a wide front end, loaded 18.4x34 rear tires and some wheel weights that got the tractor weight over 10,000 lbs. It was a great combination. The 3020 handled it like it was nothing. We (I) mowed over a hundred acres of hay with it including 1st, 2nd and some 3rd cutting. About 250 acres a year total. The one time that I pulled it with something other than the 3020 was with our Ford 3000. It had loaded tires and wheel weights. It weighed about 5000 lbs. Power was not a problem, although it did make it work a little. The main thing was the weight of the machine. You definitely knew it was back there. It would be a real problem in hills.