I think you're asking here if she saw any cows when she visited a farm. That is, any of the cattle that live there. A simple "Did you see the cows?" would suffice, in my opinion. There's nothing wrong with the first two answers. I'm just trying to keep it simple and natural sounding :)

(I personally would suggest you keep the "any".) From my point of view, if you do not use "any" then you are assuming that the cows were there and just want to know if the person saw them. But if you use "any" then you do not know if there are cows in that farm.

Either way is technically correct. "Did you see any cows on the farm?" This is either skeptical or colloquial; it's more natural in my opinion, but whether it's skeptical or colloquial depends on the emphasis. If the speaker emphasizes "any", I would say that he's being skeptical; if he emphasizes "cows", then he's just being casual. "Did you see cows on the farm?" This puts the emphasis on cows. You might have seen pigs and geese and chickens on the farm, but what we're really interested in is the cows. Of course, verbal emphasis could change the meaning. Some examples of verbal emphasis: "Did YOU see cows on the farm?" (or was it someone else?) "Did you SEE cows on the farm?" (or did you only smell them?) "Did you see COWS on the farm?" (or were there only horses?) "Did you see cows on the FARM?" (or were they only at the petting zoo?) Generally, I'd say that without "any", it's more easy to add emphasis, whereas with the "any", it's more colloquial and natural. But the difference is quite subtle and it depends almost entirely on verbal emphasis.

Thanks!

....ON the farm Not IN the farm