Well, what I'm gonna plant this year is a mix of white clover and rye, it would work either way. Rye is used as a second crop and is best planted at the end of Aug. here in WI, the clover can be planted then as well but you will not see any of it till the following year because it focuses on it's root growth first. So rye would be a good cover crop for it.
Oats would work as well but dies off with the frost.
White clover especially durana grows in shaded areas better than the others.
I'm assuming its a deciduous forest or hardwoods so when the leaves drop it'll get more sunlight and should work.
Being a smaller in woods plot I'd spend the little money and put down some fert and whatever is needed to optimize your odds.
Genesis 27:3 Take your bow and quiver full of arrows out into the open country, and hunt some wild game.....