Build near farm/cow barn/cow pasture

I would ask the immediate neighbors .... I would be more bothered by the tractors etc. than by the cows and flies ...

Can't say much about farms and cows. I once lived wall to wall with a small stable (<=4 horses). Never again. In the village, I also developed an animal hair allergy*. But maybe I'm just different.

*Fortunately, it turned out to be very selective. Luckily, I don't react to the current furry friends my partner brought along.

As long as the cows are allowed outside, everything is great. A barn next to it is still better than a field that is regularly fertilized. I would also check it regularly/look/smell/listen to it.

You summarize it well yourself. It seems to fit.

No, the following doubts were raised:

But whether that’s too much land for us, I really can’t estimate right now...

I would be more bothered by the tractors etc. than the cows and flies ...

Phew, here you can clearly see the different views: I would probably be bothered by the flies, which you can’t control in large numbers. Tractors are also not in the field for 10 hours a day. Then there are the smells... personally I wouldn’t mind those. You have to weigh whether you have a sensitive nose. So: go there, smell, listen, look! Again and again!

You have to like it. I think farms are great

Wouldn't bother me. Better a cowshed with rural soundscape than an apartment block with party-loving people.