The idea that wild stallions "steal" mares is a basic one - but the truth is far more nuanced.
Many years ago I was riding on either Dartmoor where they run ponies out. I was on a larger pony mare who happened to be in heat. We rounded the corner and there was a breeding band complete with stallion.
The interaction which followed was a little scary, but interesting to watch. The stallion immediately began display behavior - which in stallions is the head and tail coming up and trotting with exaggerated action, intended to make him look big, impressive and show off how he can move. (We channel these same motions into advanced dressage, most particularly piaffe and passage).
The mare I was riding, who was probably horny as anything, started to sidle towards the stallion.
One of the mares in his band took up a station between him and the band and...you know what they say about mare face?
I have never seen such mare face. It was very obvious to me or any competent horse person that she was saying "You come back here right now or you are in real trouble."
One of the wranglers rode at the stallion riding a whip and between that and the looks he was getting from his "queen" he decided not to try anything further and trotted/bounced back to his harem.
I did not see "snaking" behavior, which is how a stallion herds mares (and how a trained horse herds cows, quite interesting to be on the horse when they do that) but I don't think he got close enough. However, the interest of the mare in the stallion was equal.
"Stealing" of mares often occurs when a young stallion approaches a dominant herd. However, in wild interactions, most of the "stolen" mares are actually the fillies born in the herd - because the dominant stallion, if he hasn't already simply chased them off (or their mothers haven't) is able to identify them as his own offspring and won't breed them. If another male shows up, then the dynamic is often that the male will be allowed to leave with a daughter or two. (This is how horses avoid inbreeding).
Stallions will though approach domestic mares, and the issue is often that the mares are without a male presence or the only males present are geldings, whom the stallion sees as subservient. From his perspective, he's assuming (as with the mare I was riding) that these mares are either young fillies who left their own herd, or part of a herd who's stallion has been killed, so of course he's seeing an opportunity to impress (hence the display behavior) these unattached females. What we see as "stealing" is, of course, simply courtship - a mare who doesn't want to be "stolen" will give the stallion a solid kick for his troubles!