Interesting question. Does seem at least possible that a splitter could be run on batteries. Would really be interesting if it had somewhat of a solar 'dog house' to protect all the vital equipment from weather, but then the solar could charge the batteries in the 'off' season use. Of course that would also be the big downside for me - a battery splitter would need a modest (in both size and cost) battery pack, but if that pack is 'only' dedicated to the splitter, seems it would spend a lot of time sitting... at least at my place. When I get a load of wood, I process it. but in an average year, that could be 3, 4 or 5 times which could be a weekend of use for the splitter 5x per year... sitting the other 47 weeks.
As far as battery/electric power, it might be convenient to consider splitting the wood and work up from there vs working down from a gas engine. If you know the average force applied, the length of the log and the time you want to spend, that is literally the 'power' equation. You just have to come up with good approximations of each!
Example:
Force: Well, I have a '30 ton' splitter, but I doubt it goes that high very often. Seems like a lot of people split a lot of wood with small splitters in the single digit ton range. So maybe 8 tons on average, 16,000 pounds?
Distance: I cut wood about 20" long. Most logs seem to 'split' when the upper half is penetrated, so force applied for 10 inches on average
Time: 'Cycle' times of 10 seconds are pretty good, so maybe 6 seconds on the split and 4 on the return
Punch that into an online calculator because it is early and I am lazy... it's about 3,000 watts.
Most likely that is still too high because I would expect force to generally drop off as the split progresses. The return stroke would be almost trivial in power and with a good design, if you aren't splittin' you aren't drawing power.
But either way, a 3KW burst for 6 seconds is certainly in the realm of possibility. Seems like kids with hot rod skate boards and e bikes can pretty easily pull 50 amps from a 72V battery for way longer than 6 seconds!
So overall, seems doable, though I'd probably want a companion e-bike, e-scooter or e-skateboard to use the battery in the 47 week off period!