Find out if dock is one of those plants that grows a new plant from every little broken bit of root before you plow it.....

Find out what soil conditions dock favors, do a soil test, and balance the soil to favor grass. If you go the herbicide route, keep those horses off for a long time, be very cautious. Yourself, too. It is a poison, after all. Remember Agent Orange? Just some uneducated thoughts. I've been taking the long route with my pasture, but I have had to buy quite a few bales of hay over the years when I had a horse here.
I bulldozed, soil-tested, seeded, fertilized, limed, fertilized again, and then started comparing hay costs to chemical costs, and did some research, and slowed it down. Compost, compost, compost. Mow, mow, mow. I need more lime now, lots of acid-loving plants showing up again, but more compost would help, too, if I had access to a lot more. Chemical fertilizers disrupt the natural balance and kill earthworms and beneficial things. But sometimes a big whammy is needed to get things off to a quicker start.