Re: hobby/small sideliner
consider doing multiple things. bees and livestock for instance.
stocking rates on livestock is what they look at. In our area it is 1 cow / 3 acres average. More than that you are feeding not grazing. Consider sheep or goats. Go down and talk to the county appraisal office and ask for the ag person. As them what they require. Yes they are sceptical of 4 acres but if it is fenced and you can prove 5 years of ag use you can get it. You'll need pictures, vet records, purchase records, etc.
you could do hay but it will cost you 350 to have your acres cut and baled each time and you would be lucky to get that much back out of it if you don't have your own equipment.
Bees alone probably won't get it. Doubt you can run a big enough operation to justify the whole thing as bee ag without getting your city and neighbors aggravated. also you will have to exclude your residence.
you could also buy a couple of calves in the spring and sell them in the fall. Do that each year and show you are actually grazing them not just fattening them with cubes.
with 4 acres you have a lot of scepticism to overcome with the county. might be easier to just buy more land
"Beware of all enterprises that require new clothes"
Henry David Thoreau, Walden