Looks to be almost like a ketchum grenade, you can look at Civil War hand grenades here The Civil War Since this grenade is got "Winchester" on it.. After the war, Oliver Winchester renamed New Haven Arms the Winchester Repeating Arms Company in 1866. This would not be a Civil War grenade but post Civil War. I'd be very careful with this any drop or it being run over could explode it and in fact there are ATF laws if believe that requiring if you find something like this too notify them.
gsxraddict got it right, it's a mortar round. When I was a stupid teenager we used to sneak on to the impact area at a local army base, and pick up stuff like that. You might have a "dud" round... dangerous, in other words. If you have an acquaintance that is familiar with ordnance, you should have them look at it. But then again, maybe you should call the local sheriffs department and let them know what you found. They will probably call in EOD (Explosive Ordnance Disposal) people who will blow it up.
You would have to be a complete nutball too play around with these or even take this home.. Someone is gonna get hurt this is one reason hunting Military bases for me is out of the question...