On this it's much a case of , " You pays yer money & makes yer choice .\2".
Using your method above will like as not see you with a shed load of weeds for six or so years , as the viable wed seeds in the horse muck & soild beddings start theire everal years of delayed germinations .
Stable /horse muck is usually full of viable weed seeds not only from the horse muck as the digestion system is reasonable straight through ( unlike ruminants where it gets well & truly digested ) .
You also have all manner of seeds coming out of the hay feed.
If you can , try the " Berkley 21 day hot composting method " to the letter with your hose muck perhaps adding some wetted straw as a bulking agent .
Runinant poop is good ,as their digestion system is much more complex.
So sheep . goat and cow don't have much weed seed content unless there is a lot of hay being fed and it gets trodden into the bedding .
Bird poop is also a good addition to the well turned over compost heap .
In truth making a good balance compost out of dungs and other mater is quite an art and well worth reading up a dozen of so different methods from places like the American university ectension colleges or our very own DEFRA type sources ( including the Royal Horticultural Society website ).
You'll normally get far too much witchcraft , hocuc pocus & 8o11ck5 from the majority individuals blog side