I would agree with Libby, having happy (mentally) horses in the big field is more important than saving seeds at this late date. I did not seed this year because of local drought conditions. We had minimal rain all Aug thru Sept, no grass growth until Oct when it started raining again. I had to start winter hay in Sept because of no grass.
See what you get in very early spring with grass growth, night freezing, do check soil temps wit a soil thermometer. Seed won’t germinate in cold dirt, just rots… You can try seeding your bald spots, thin areas then. Try to go early, for better rain if it heats up for summer. I get better germination if I do some light discing, fertilizing, seeding, then dragging, to get good seed contact with the soil. I have smaller fields and often spread the hay storage sweepings, some bales of straw thru my full sized manure speader to cover the dirt after dragging. I love those little sprouts coming up thru the cover! Cover helps prevent birds eating my seed too. My seed costs a mint, I feel like I am spreading gold dust!! I want every seed to sprout and survive intoto being a plant.
As a bonus, the discing, dragging, help smooth the dirt of winter hoof prints for MUCH smoother mowing later. It does look a bit rough when you get done, but it seems all the cut up grasses, most seeds, take hold again to grow well into nice fields. I would do the work, spread seed, drag when rain is expected soon and more rain in the next few weeks for keeping your seeds growing. Check several weather predictions!! Even the Almanac can beat weather stations some times. My local computer ones are useless. The computer ones say sun as the rain is pouring down! Maybe you know someone with some accurate predicting aches or pains to help the timing! Ha ha
Weather is going to do as it pleases, it is a big guessing game to time things right. Good luck come spring.