Live cover is always risky but its usually the mare who gets hurt. Ive seen mares get savaged by a stallion and die from sepsis shortly after. This is why virtually all high end horse breeders use envitro
I have bred my mares to other peoples studs. As mentioned the mares if were not totally in heat were hobbled. I noticed a baby squeaking and running around. It should have been put up out of sight. I have seen studs get kicked in the chest and shoulder, but these were very experienced studs. Usually the mares were cross tied and hobbled. A shame what happened, surely a teachable moment.
When I was in my 20's, I helped the local horse trainer/stud owner as he was much too old to be handling this sort of work. At the time I was literally afraid of NOTHING but between the 'excited' studs and the often only marginally receptive mares, that was every bit as dangerous as the flying bullets had been a few short years prior. I hobbled a lot of mares to prevent injuries to the studs (and handlers) and with some amount of luck came out unscathed in the process.
One of the studs was a 'biter' and took a palm sized chunk out of the owner putting him out of action for several weeks. When he was able to walk back to the barn, he noted that stud was a wee bit touchy about being haltered but no longer showed any inclination to bite. The old man didn't say a word to me about my correction technique or even a comment as to what might have changed the stud's attitude. Guess losing a 3" diameter chunk of skin and muscle from his upper arm made him a bit more tolerant of my sometimes brutal actions.