There are exceptions. They are notable for being exceptions.
"Independently-owned farms" are the exception, these days, not the people. Every single one I've ever seen has at least one guy on there that performs miracles with PVC pipe, a TIG welder and spare bits of iron.
That depends greatly on the farm in question. I grew up on a dairy farm, and there was no such thing as a break from work unless we hired someone to take care of the cows for us. They are fairly constant in the amount of work you have to put in (I imagine other livestock are similar but that's outside my experience).
That might be the case for you.
I do all my best programming when I'm driving a tractor. When I stop, I just need to type it all in.
Or, driving my car, for that matter. I just need to get from here to way over there, it's maybe 90 miles, something like a two and a half hour drive, during which time no-one can phone me, no-one can come up and hand me something that's Clearly My Problem Because It Has An Electrical Connector, no-one can ask me what's wrong with the printer in the facilities office, and I can just sit and quietly think. I don't even have to put up with braying adverts on the local radio station.