Yup, as long as the cow is there and the green fumes are flowing, anybody and everybody downwind will be grossed out. I don't know the exact duration of the effect after leaving the AoE, but IIRC it's quite long, around 5 minutes or so.
That's PBI's point though, I think : the cows are usefull on an open battlefield, because you can drop them in the path of an advancing enemy. Keyword being advancing.
In a siege situation, I wouldn't say the cows are particularly worth it, for the reason you mentionned. Besides, it's much more fun/effective to concentrate fire to try and crumble a wall beneath its defenders, or just park them down a street and fire at the town square. One boulder is bound to be a lucky hit amidst the hail falling over every building in a 120° arc. Anyway, nobody ever said siege weapons were useless in sieges
For what it's worth, I have the same qualms about hornet throwers in the Americas campaign, I can't seem to use them in a way that would ensure the hornet would only affect the bad Spanish guys :/
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