There is absolutly nothing wrong with overseeding a winter annual into your pasture. rye, ryegrass, oats, wheat, would all be good choices - probably like the oats or ryegrass option best. You could probably get by with spreading the seed with a broadcast spreader or by hand, but if you want to do the job right, rent a no-till drill from the local co-op or NRCS office. Put the seed in about 1/2" deep and you are set. You do need to put down some fertilizer as well. If you have been using this ground for pasture for several years and have been spreading manure on it, you may only need a little N - at least 50 units. The biggest thing you need to check is pH. You need your soil at least at 6 - preferably at 6.5pH. Lime accordingly. But, if you aren't going to check your pH and fertilize and lime accordingly, don't waste the money on the seed - Just buy hay!
We have seen a lot of horse owners over the years get all excited about rotation grazing, new and exciting grasses, pasture renovation, seeding horse pasture mixes, etc. Sometimes they are in a position to take advantage of these practices - most of the time they are not. If you already own a lot of farm machinery, you may be able to make it work, but buying 20K in farm machinery to renovate 2 acres would buy a lot of hay for many years.