Horses are selective grazers. They don't keep anything eaten down nice and even. They will ONLY eat certain things in the pasture mix and ignore others, and when given enough land, the will make manure in one area and let everything in that area grow and get long, and graze another area down to nubs.
Mowing and/or bushogging regularly is one part of good pasture management. It encourages the good grasses to grow and spread and choke out the weeds, and cuts down the weeds before they have a chance to seed.