I think most people know a western has horses and is set in american west between 1820-1900.
Or is set in a different place and time and emulates the tropes of the Western genre, such as Outland
or the cartoon BraveStarr
Heck, I even think of the 2006 NYC-set thriller 16 Blocks
as a sort of Western.
And don't forget Once Upon a Time in Mexico
, I agree: "Adam Sandler comedy Western" sounds like the pre-conception murder of humor, Terminator 1