I think his reaction is a combination of a lot of things. It's not as obvious in the movie, but in the story, it is implied that he was chosen for her by her father as a husband. She doesn't find him attractive at all, nor does she like him, and being selfish and sadistic, she enjoys torturing him. She strips down in front of him to insult him. He tells her she looks like a "slattern" (gotta love that word) for being barefoot, so she takes it one step further. "Oh, my bare feet bother you? Well, get a load of this!"
The look on her face says it all, that little smirk. He reacts violently, yelling that he'll kill her because he desperately wants to do just that, but he knows that in fact, he can't. He's a discipled military man, unemotional & strong--not one to be pushed around by a mere woman. But he can't do anything about her behavior, and he can't tame her. She has won again. (And don't forget, he knows he's being cuckolded by his wife and his superior officer.) He just loses it. He hates her with every fiber of his being.
He beats the horse because the horse mirrors his wife's wildness. He tries to tame the horse and the horse "insults" him by running wild, just like his wife does. When he realizes what he's done, he is horrified by his loss of control. And realizes that no matter how hard he tries, she will always win. So he goes back to the party and accepts his defeat by allowing her to beat him.
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