Digger, I didn't mean to be alarmist!
I think someone would have to try pretty hard to get ill from manure, dedicatedly smacking themselves in the face with a fresh horse poopee pie every day.
At any one time, a very small percentage of horses (and humans, for that matter!) is carrying a disease that could conceivably jump to a human, like salmonella, e. coli or giardia.
These things can spread in fresh dung and urine, but please refer to my earlier poopee pie hypothesis.
Seeds of weeds that the horse ate are much more likely to be an issue in fresh manure.
Anyway, I think we all agree: the way to treat manure is to let it wait and rot in a big pile for a good stretch, until it pretty much looks like really soft crumbly soil.
Air is the key to composting manure quickly:
The lazy-eco way is to bury pipes into your big pile. The pipes have holes (about 1cm in diameter) drilled through them all the way down their length. This will improve ventilation in the middle, helping it rot & dispersing the odour.
The get-fit-eco way is to reverse your pile now and then with a fork or spade, turning the outside of the old pile into the middle of the new pile.
And the really fast way is to use a digger!