I know most people are suggesting the use of batteries and solar charging but if you were contemplating running an overhead wire, you might consider running a few Ethernet cables connected to a PoE switch and PoE to USB adapters. PoE (Power over Ethernet) is low voltage and has the added benefit of allowing you to add a Wifi AP for mobile devices to connect to. Convoluted tubing could be used to help protect the Ethernet cables. Ethernet has a 100 meter limit so you should be on distance.
I am not a contractor so I don't know if this violates any codes but thought this could be a nice alternative to running 120v.
POE can supply about 15.4 watts of power on a normal port, but there are newer standards that can supply 30, 60, or 100 W (which works out at 12, 27, 53, or 73W delivered at the device)
Voltage on the UTP cable is somewhere between 42V and 57V, but there is a "negotiation" protocol so the wires are not live unless there is termination equipment detected on the end.
Jargon: there needs to be a POE Injector or a "midspan injector" in the house which is connected to 120/220V mains AC. This box has two RJ45 sockets, one for data in, and the other for data+power out. You can use it without a data link. These range in price from $40 to $hundreds. Or it is possible to get an ethernet switch with this injection functionality but the costs start increasing.
from https://www.gowifi.co.nz/power/active-poe-injectors.html
The other part is a POE Splitter which does the opposite. This example gives a 5V DC supply on a barrel plug, but versions exist that have mini/micro/usbC. This functionality is normally built-in to higher end devices like APs or desk phones or cameras. These separate items are about $30.
from https://www.gowifi.co.nz/power/gaf-5v10w.html
Another advantage is that the UTP cable can be wound up when the kids aren't using the treehouse. Cat5 cable is cheap and you could just leave it out. The only parts that have to be kept dry are the splitter and the injector, the wire between them can get wet and it will still last years before it deteriorates. You can even run it on a catenary wire or direct-bury or just leave it on the surface (though it might be a trip hazard)
