It seems that what you are really renting out is storage space. It just happens to be in a barn located on a farm. I could easily make a case for reporting the income (and any associated expenses) on either Schedule E or Schedule F. If you are already filing Schedule F for other farm income, I would suggest including the rent on that form. If you are living on the farm but not actively engaged in farming, then Schedule E is probably easier to complete for the rental.
For Form 1099-MISC purposes, I would certainly consider that to be farm rental income.