Don't know about the knowledge, just passing on what little I've learned about a few things.
Too bad you didn't speak up late last summer. I'd have suggested sowing a cover crop on what you turned over, and disked up. Something like Oats, or Buckwheat sown on fairly heavy would have suppressed any weeds, and killed by the winter cold. Sown late enough, it wouldn't have gotten that tall, but enough to not worry about erosion. Then come spring, enough open earth to still frost seed. It would have also given your new grass a little kick from N produced decomposing. Oh well...
Don't know I'd use the Glyphosate at all, period. But that's me. I use it around buildings and parts of the driveway, but that's about it.
It won't do any good, unless you have plants growing. And depending on the rate, if applied heavy enough, some of the extended types can keep anything from germinating for up to 4 months.
If you've got the pastures worked down pretty decent, and the freeze/thaw has mellowed it even more. If it'd be acceptable for the finished pasture, I'd just Frost Seed it. If it's still pretty rough, wait until it's workable, get the finish you want, sow the seed, then go over it with a cultipacker, or some sort of roller to set the seed in.
Again, if the grass seed is sown heavy enough, it should choke out the weeds. If some do come up, mow it off before they go to seed.
Guessing you'll have to watch overgrazing the new seeding too. Horses having upper teeth have the ability to nip grass right down to the ground, and even pull it out by the roots. Where as cattle with no upper teeth, and just able to pull & twist it off, usually leave about 2" of established grass.
And another thing... Do not turn them out on lush grass..!! I found out the hard way last year, even though I just let them out for an hour, up to 8-10 hours over a period of two weeks the first of April. I had two within a hair of foundering. I waited too late to turn them out, hoping to let the grass get ahead of them a bit, as I reseeded in the fall, even though it was formerly part of my hay field. Just wanted to sweeten it up a bit.They simply gorged themselves, and new growth grass is close to 21%+ protein. This year they will be turned out as soon as it starts greening up. And after any frost that may be on the grass, melts off. I ended up feeding out all of my first cutting hay, which was a little shy anyway, due to cutting it early, to keep them off pasture for 14 weeks, until they were sound enough to go back on pasture.
So clipping the new growth grass won't hurt a thing, if you see weeds growing, and clipping before they go to seed. It should be well established by then.