If I know mine are going to be sitting for an extended period of time I shut the gas off with them running and let it run til it dies so I won't have old gas in the carb.
So here are my experiences with towing a splitter alone. My dad used to have an old horizontal splitter that was kind of low to the ground. I had a guy run into me at a stop light because he "didn't see it..." He hit the hydraulic tank and didn't really do any damage but from then on I started towing it on my trailer. Then, my nephew and I went in on a brand new Oregon horizontal/vertical splitter (I have tons of complaints about this product, but below is the one thing we can relate directly to towing). This thing is pretty tall with larger tires, etc. so we figured it was no problem to tow it. If you look at their design, which most of the Speeco spin-offs use, the hydraulic tank is horizontal and serves as the axle mounting location. They basically weld the axle to the bottom of the tank. We developed a leak where the tank and axle meet. Orengon replaced the tank under warranty but a few months later we had the same issue. We concluded that because there is no suspension, the splitter, as others have mentioned, takes a horrific beating being pulled down the road. New England roads makes it worse.... We think the leaks were caused by stress fractures from the wheel transmitting the bumps and jolts through the axle. We repaired it ourselves and added some additional bracing the second time it happened, but we basically trailer it to and from each other's house now.