Build near farm/cow barn/cow pasture

It's all a question of habit, I would say. It wouldn't bother me, but I also grew up in a small rural town and am therefore probably rather insensitive.

I wouldn’t mind either. There are much more annoying things...

Cows are less of a problem. But pigs and silage are an absolute no go.

Where do you live now? City or countryside? A farm always means noise and smells in many different forms.

It's a matter of preference. We have all become quite pampered "mimimi" prosperous invalids who tolerate traffic noise but are bothered by insects and animal sounds.
If you move there, you'll have more insects and flies, animal noises, rural olfactory stimuli, and operational sounds from the farm.
Weighing it yourself is the only sensible thing to do. Camp on the property for a few days or park an RV there..

I find cows okay in terms of smell, but pigs are not acceptable to me at all. You should also be aware of all the operational processes. Work is not only done from Monday to Friday from 7 a.m. to 4 p.m. They also work on weekends and sometimes around the clock during harvest time. Any planned [Betriebserweiterungen]? If you see too much negative about the construction site, then forget it. If you think you can come to terms with a few minor things, then go ahead.