Western culture generally doesn't depict women's being behind the plow in entertainment, art and literature.
Agriculture, as opposed to transhumance/long-range livestock herding and hunter-gatherer societies, is more favorable to women, though, because of its domestic nature. Women like to nest as men like to roam.
Just keep in mind, there's a helluva LOT of western culture fiction gets entirely wrong... which... I guess is par for the course since it's... well. Complete Fiction.
In defense of the umbrella point you're making though: At least in Oklahoma and Texas, from my own observations and those of my husband - Women did NOT haul horses and camp with horses, and haul them around for riding in such great numbers as are seen now... unless they were rodeo competitors. Barrel Racers and Mom's hauling kids to playdays and Granmas hauling grandbabies to play days has always been a thing too - but NOT in as great of numbers as we see now.
That said: At a ranch rodeo or rodeo-rodeo, you will see an ish ton more men there on horses than women, but that's changing. I'm seeing more female ropers and bulldoggers than I have in the past, there's more at every rodeo I go to, and there's more girls at the junior levels than ever before - and they're roping, pole bending, barrel racing, etc.
I can also relate a story from about a month ago. I haul solo to go camp with the horses. I meet other women there, wherever there is. On my way to a new place we'd never been, I stopped at the intersection of two Oklahoma highways. There was a very senior gentleman in a 1 ton feed truck that went by - I had to wait on him to pull out. He was hanging a HUGE THUMBS UP out the window, and the the biggest grin split his leather, tanned face. I waved and gave him a thumbs up back. I was telling T about it and she was just cackling. Her 9 year old daughter asked why he did that, and why it was funny.
T explained she was guessing, as was I, that back in his day, the majority of women didn't haul their own horses or do as much with horses without men there with them, that times are changing and women are becoming the majority of horsemen now, we're not content to wait around on our men to help us haul and go camping, and the gentleman that waved was maybe showing his enthusiastic support for a woman, hauling horses solo, on the backways of Oklahoma.
My husband and I, both born in the 70s, have talked about this as well. Until the last 10 years, we cannot recall seeing as many women, hauling solo, going to rodeos solo, or going trailriding with other groups of solo hauling women. You just didn't see women, without men doing the hauling/driving, or being present until the last ten years... with the exception of barrel racers, moms & granmas hauling kids to playdays and youth rodeos.
Now, let's go further back. Way back. Horse and Buggy days - women did pretty much everything men do. Why? Because the survival of the family absolutely depended on it. There wasn't room on the American Frontier for a whole of lot of Male Roles and Female Roles. There wasn't as much of it even in the 20s and 30s... at least not to the extent written fiction and Hollywood would have you believe. That's more of a 1950s and 1960s portrayal (Think Gunsmoke, Rawhide, John Wayne movies). Women were the damsels in distress (True Grit being an exception), the rancher's wives, the farmer's wives, the church going righteous and pure sorts relegated to washing laundry and cooking.
In truth, they were often in charge of home defense, taking care of the livestock, plowing, driving the buggy teams, and many other horse or cattle related chores necessary for the survival and well being of the family. Caveat:I'm talking about pioneer women and those who came west seeking the more liberal mindset of the American Old West. The idea that women in the old west were to be guarded and treated like wilting flowers and that they didn't do 'man jobs' especially with equines, is a myth.