A “pull behind mower”? Do you mean like a hay mower? A brush hog mower is not like a hay mower. Hay mowers may be “sickle bar” or “discbine”, but they are primarily for mowing grass for hay, leave it in a windrow. Not really suitable for mowing a pasture, IMO. A brush hog is a very indestructible beast of a mower, hard to kill. It mounts onto the back of the tractor via the 3 point hitch, and runs off the PTO, but is not a “tow behind” implement You can pick it up, and carry it around, then lower it and mow and pick it up again as necessary. It can go through and successfully cut small saplings, and “brush”- crap that will grow up in your pasture (and weeds) that your horses don’t eat. If you don’t mow this stuff down, it will spread healthily, and take over your pasture with inedible weeds. Mow each field as you rotate horses out of it and into fresh grazing. Brush hogs are fairly cheap to buy, hay mowers can be expensive to buy if they are newer and fancy, older ones are probably worth twice what a decent brush hog is. If you are sure that you are not going to hay this land, sell the mower if it is not a brush hog, but instead is a mower suited for haying.
If snow removal is not an issue for you, a cab tractor (with heat and AC) may not be necessary. Just a roof top on an open station tractor is workable to keep the direct sun off you in summer. We made one for our big JD open station tractor (1976 tractor 14,000 hrs on her), out of some 4 X 4s and plywood. It works great, and way cheaper than buying one from the factory. Just fastened the uprights to the roll bar of the tractor, roof extends forward from there. DH isn’t the greatest carpenter in the world, but he got this construction job done just fine! So don’t automatically dismiss an open station tractor, when a roof is so easily and cheaply fabricated. If not by you, by someone handy.
I do the pasture mowing here on our farm, with the 32 horse Kubota, and a JD brush hog. I also run the hay rake for all the fields, and bale with the small square baler when we use it. I have no cab, and no roof, open station tractor. But I am OK with just a hat and some sun screen in summer, a cool drink wedged next to my seat, and a long sleeved cotton shirt soaked in cold water from the hose. The heat doesn’t bother me much. Some of our “pasture” is very rough, never before mowed or cared for, a bit like riding a bucking bronc the first few times mowed- getting better and more civilized over the years. If your pasture has been previously hayed, it should be pretty easy to mow, and shouldn’t take long either, not a big job.