The term "open" or "closed" refers to the main inlet/outlet ports on the valve. It is usually refered to as "open center" or "closed center". On a open center valve, the fluid flowing into the inlet flows unrestricted to and out the outlet port when the valve is in the center position. When the valve handle is moved away from center, the inlet flow is directed to one of the working ports that would move a cylinder or motor. The system pressure then builds depending upon the load on the cylinder up to the maximum pressure allowed by the safty bypass valves. The other working port is silmultaneously connected to the outlet port on the valve to give the fluid from the other side of the cylinder someplace to go as the cylinder or motor moves. When the valve is moved the opposite direction from center, the inlet flow is directed to the opposite wirking port so the cylinder/motor moves in the opposite direction.
A closed center valve is just that, closed from inlet to outlet in it's center position. Some types of cranes use this type valve in conjunction with a system that maintains a constant high system pressure.
Most tractor systems use open center valves as this places no load on the system(hydraulic fluid is flowing but at very low pressure) untill a lever is moved and some work is being performed then the system pressure varies based upon the work being done. As soon as the work is finished and the lever is returned to center the load is taken off the engine.
It sounds like your tractor already has a control valve on it that controls pressure to a set of ports on the rear of the tractor? You may not need any other valves, the splitter cylinder ports would connect to these ports and you could control the cylinder with the valve on your fender. This however may not be the most efficient for splitting as you have to move to that fender mounted lever to split each log. Most logsplitters have the lever close to the cylinder for convenient ops. It is also safer as the person splitting is the only one who controls the cylinder. In that case, you would need a open center splitter valve(available at northern tool) and connect it's supply and return to those ports on the tractor. You would then use something to hold the fender lever engaged all the time that you are splitting, to supply pressure to the splitter valve. The splitter valve would then be able to control the splitter cylinder.
Simple huh

If you ae not familliar with hydraulics, this might be a good queston to take to your local hydraulic shop. You will most likley need some type hose/fitting fabricated to get this all working and they will probably be able to give you some advice on how best/safest to accomplish this.
Good luck and post a pic of what you wind up with.