I have taken a very quick look at Tarrytown's
zoning chapter and it doesn't appear to allow for a lot of agricultural use.
The
Planning & Zoning department there could help you more.
Maybe there are other municipalities in Westchester that would suit.
Westchester County Planning would be a source for that information.
If the price of real estate is of any concern to you, you might consider looking a county or two northward from Westchester.