"You do not want horses."
Translation:Jij wilt geen paarden.
Based on my knowledge of German, the suggestion you're proposing would be extremely rare, and here's why:
Let's say that you're trying to convince someone that they don't want horses, they need horses. It's most likely that someone has already mentioned horses at this point, so you can replace the noun with a pronoun. The result will be, "Je wilt ze niet!" or, more likely, "Ze wilt je niet!" (in German word order, at least. Sorry, not a Dutch expert yet).
In this case, since the object of the negation is a pronoun rather than a noun, "niet" is grammatically correct. The message is conveyed, and no strange niet+noun combination is used. The niet+noun combination sounds strange to my German-trained ears, and I imagine it sounds just as strange in Dutch.
When in doubt, always use "geen" to negate a noun, even if you're stressing the verb. You'll never be wrong, and you can clear up any lingering ambiguity with a follow-up statement.
For those whom asked why it's not "Jij wilt paarden niet"; a good(general) way to remember is:
You'll use "niet" AFTER the object, IF there is a "de/het" BEFORE it. ".... de/het [object] niet."
(Subject) NIET (verb)
"geen" replaces "een", and is used if de/het doesn't appear before the object. ".... een/#/_ [object]." becomes ".... geen [object]."