It is best to use manufacturer recommendations for the fluid for their products until the warranty runs out, and then if you have the knowledge to interpret the
labels you can find something more suitable.
Hydraulics seems to work well with a large variety of fluids, such as ATF, motor oil, and blended fluids such as HyTrans and the rest of the pack.
My PowerTrac uses10W-40 engine motor oil as the hyd fluid, and has been using it about 20 years. It seems to work very well, and can be found just about anywhere.
Case equipment seems to like HyTrans, but they allow ATM or motor oil as an option.
If the log splitter is a 3pt splitter, it will use what the tractor uses.