My $0.02, it depends.
How has the pasture been? How do other pastures around it look? Are they growing the density, types, and nutrition you want? Whereabouts are you? Answers are likely different in lowland Arizona vs the PNW. How critical is the nutrition of your horses?...are they breedstock or rental horses for a summer camp? Healthy vs peak performance have different needs.
I generally lead toward 'No off property amendments', but for cattle or horses I will chain harrow the clods at the end of the dry season to allow for faster breakdown of the road apples. I'll also drop any of the scrap vegetation on the property as well, whether composted first or not. If it was massively overgrazed or abused then that'll change things as well.
If I'm in an area that is 'especially anything', especially dry, especially wet, especially high or low in some mineral then I'll reconsider. Often I'd start with looking at a soil map for the area (such as
USGS Web Soil Survey or
USDA Soil Survey Map if you are in the US) and then look at the general conditions for that soil type to see if it is lacking in something. If so, then I'll consider adding something, or break down and get a soil test to help decide. For example, I use sweet lime and overseeding in one part of my North Pasture to knock back creeping buttercup, but in my area creeping buttercup is an indicator of an acidic low calcium soil.
If the pasture was abused, then I've got some choices to make. I'm assuming sustainable stocking densities here, not stockyard levels. If I'm not in a hurry, I'll bring in additional good quality hay and try to get as much the poop and urine into the pastures as I can. The chain harrow and the weather will do the work, but it'll be seasons. If I'm in a hurry, see above: soil map, soil tests, and amendments.
If there are some 'peak performance concerns', like you're raising competition horses or high end PBR bulls or something, then it is no holds barred...tons of money goes into them...but then I expect folks would also be supplementing with the finest of everything they can find. That's just not me. :)