@Stacy309 They are a bit vague about what exactly constitutes a "shared space," but if the farm grounds are part of the listed space, or guess must pass through them to enter the home, they should qualify.
In practice, though, Airbnb gives guests broad latitude to call any untrained pet a "service animal" and take it with without prior notice to a home with a no-pet policy. What this means for you is that self-check-in is not a good option - you have to meet the guests on arrival and keep an eye out to make sure they're not smuggling in any dogs, and also be prepared to turn them away if they are. In doing so, you would likely forfeit the payout for the booking, risk a retaliatory review, and might have to go through customer-support hell to prove you have legitimate cause to refuse emotional support pitbulls and keep your listing from getting suspended.
Hopefully it won't come to that, though. As long as you don't use Instant Book, you can have this discussion at each request and accept only guests who earn your confidence that they'll obey the necessary rules of your farm.