In most cases these fields are left or put into rest and then have the muck spread on and then it gives it that time to rot down, normaly fields get harrowed a week or 2 after just to rake up any loose stuff and gives it a cchance to rot down too.
If horses have to go straight back on i cant see it being a huge problem, its upto them if they eat the poo and shavings.
depends on what type of muck has been spead? pig sh.. chicken sh.. or good old fym? wouldnt ever dream of spreading the horse muck heap on the field! kind of defeats the object of pooh picking....