Every time someone posts a question like this, it seems like the majority of people post about how awful it is to just spread your horse manure through the pasture and that the only acceptable solution is to pick the poop up and dispose of it - although some will say compost it and then spread it back on the pastures.
Yet, if you actually do some research on the subject, look at extension service reports and such, the majority of experts seem to recommend dragging your pastures to break up and spread manure around. For example:
University of Minnesota:
To ensure that pasture plants can more easily use the manure’s nutrients, frequently drag or rake the manure deposited in the pasture. This will more evenly distribute the manure and promote its breakdown while also reducing the potential exposure of horses to internal parasites.
And this from the University of Missouri:
Some concern has been expressed that dragging pastures may increase the likelihood of spreading infection of intestinal parasites to grazing animals. While this may be a concern in some environments, it is generally not considered to be a problem in the Midwest and Upper South. Manure in dragged pastures dries out very quickly during most of the year (May to October) in Missouri. Exposing more manure surface area to the sterilizing effects of solar radiation kills most parasites. Simply drying the manure out reduces the likelihood of some survival for some organisms.
A quick google search turned up similar advice from Oregon State University and the University of Florida.