You could get the tin man from Wizard of Oz or rig up some sort of lubrication tank on the side of your winch tower and use some of the old motor oil you got kicking around...
Thats probably what it would take, maybe grease would last longer. This is a vertical splitter but I like standing up so I keep it horizontal. this winter I'll bring in the shop and take the wedge apart, looks like 8, 1/2" bolts holding it on the beam, I think most vertical splitters are the same way...