Sorry, my question wasn't very clear. In english, you wouldn't commonly say "The farmer has no horse". You make "horses" plural just to be grammatically correct.
So in Dutch, is there a difference in meaning between "geen paard" and "geen paarden" ?
Ahhh, on that bike! (Dutch lingo, thought you might like it :D)
Simply put, geen paarden means that the farmer has no horses at all. Geen paard is used when referring to a single/specific horse. Eg.
Heb jij een paard dat ik kan lenen?
Do you have a horse I can borrow?
Nee, ik heb geen paard, sorry!
No, I don't have a horse. Sorry!
So you'd say Ahhh, op die fiets! when you realize what someone meant? :D Geweldig!