Marty, I would have to disagree with you. My stallions are expected to keep quiet and behave themselves if/when I walk them past other horses. If I were taking them through a group of mares I would attempt to make the mares stay back to give the stallion some room, and I would still expect the stallion to pretty much mind his manners and never mind trying to talk to the girls. Why? Because I drive my stallions, and that means I may be driving them past the mares on the other side of the fence (would not drive in the pasture with the mares!) and the stallion is supposed to remember that he is working and when he is working he is not to be socializing. I do not need a harness horse to be talking and jumping around just because there's a mare on the other side of the fence. If he's loose, yes he can do those things. If he's being led or driven then no. As well, I sometimes show my stallions, and therefore they must behave even when in close quarters with other horses, mares or otherwise. It isn't just going out in the show ring, it's the close quarters in the barns as well. Waiting for a class, walking past other horses when going to/from the ring, the wash racks, leading to the stall or out of the barn to the trailer...you can end up having to walk past other horses & very close to those other horses. I expect my stallion to walk past these other horses QUIETLY--no leaping, no striking, no talking, no squealing, not even any whuffling noises. He can look and flare his nostrils but there better not be noise! so in view of all that, yes I would discipline my stallion in the situation described here.
Would I strike him that hard 3 times across the legs? No. I don't believe in using a whip on a horse's legs or face. I will smack him across the chest, or shoulder, side or hindquarters. I'll time it well and smack him once--one well timed smack is usually plenty, especially for a horse that knows his manners and just forgets them. He will accept that discipline and respect it. A younger horse might need a couple smacks--the first one sometimes doesn't have much effect, but the next one gets his attention. a crop with a popper on it may be more effective than a plain lash type of whip--it will give them a stinging smack plus make a good noise, and the noise will often get their attention just as well as the sting does. I'll often just hit the ground with the whip--the noise of that is enough to get the attention of most of my horses, and they'll pay more attention to me after that.
If it were me taking a stallion through the group of mares here, I would expect to be controlling the stallion with the lead shank, and though I would carry a whip that whip would be mostly for chasing the mares away and keeping them back a bit to give us some room. I really would not expect to have to use it on the stallion.