there colud be a big problem for you hiding in the back ground ....Horse muck manure usually contains zillions of viable weed seeds even after being left to rot in a big heap by your stable for a couple of years .
Adding some to your compost heap to bring in beneficial bacteria ..
There will be plenty of still viable seds that won't get killed off even in your garden compost heap unless up practice a method like the Berkley 18 day hot composting method
It's all to do with how horses intestines work , they don't process the fodder like ruminants do so most seeds pass through the horse intact .
Cow muck & wheat straw is one of the finest things to put in a compost heap & mix it in well then let it cook . Bullock & steer dung & urine soaked straw is a wee bit too strong & acidic so should only be used to fertilize the ground once every seven years @ 1 barrow load per square yard using the three or more year old well rotted manure
If your horse never gets free range graze or eating /bedding hay , it only eats Alfalfa & is on mats &/ or paper or shavings then the problem is much reduced .