Here in the Netherlands we have lots of plots on the outside of cities with gardens people in apartments can rent for a small fee. Friend of mine has one and we get a ton of veggies and stuff from them every year it's great. Going out to take care of it is like a day to the countryside kind of thing, they tell me.

I suppose a shed in the woods is not impossible but a lot of factors need to be just right or it gets way too expensive and/or uncomfortable. In Europe, most forests are publicly accessible and there are various tiny settlements but I suppose that's not the case in many American states.