The "Another translation" is "The farmers have horses and dogs." (With an extra space between have and horses).
This maybe the cause.
when I say peasants in English, I think of poor agrarian servants. I gather it is different in swedish?
I was going to ask something similar. "Peasant" implies a level of poverty that "farmer" does not. And in some cases, "peasant" might be used to describe someone who does not farm at all. Is this the case in Swedish as well?
Farmer is the main translation now, but just in case: I think it's just a case of language evolving (or in this case, not evolving) over time so it used to refer to what is called a peasant in English, but refers to what would be called a farmer these days. Really there's not a big difference in what they actually do, just that these days they're not doing it on the behalf of anyone above them on the societal ladder, and the financial situation is better. Just try to see the word as referring to the actual work of the person, rather than their levels of servitude and poverty.
Jason - my abridged S-E dictionary does not have bönd-anything in it, but it does have bön which is plea, supplication etc. I assume that means böndarna derives from bond (like bonded servants) and boon. Doesn`t help with current meaning, but interesting!