Pressure treated plywood exists. It's treated with the same chemicals as the PT dimensional lumber that you're probably using to build other parts of the tree house. The glues in it may or may not be especially water resistant, but it's used for exterior applications all over the place and there hasn't been a general uproar about it failing prematurely, so one might assume that it's generally suited to purpose.
You could use the PT plywood for the floor. You could also slope the floor for runoff (the standard 1/4" per foot of run would be fine), just like you'd slope a deck surface. Then, either at every plywood joint or just on the lowest edge, leave a small gap (I'd think 1/4" should do just fine) for the water to run out. This will ensure that any water that does get in has a place to get out and encouragement to do so.
I built a shed a couple of summers ago and I covered the bare (non-PT) studs with T1-11 siding. This is also a PT/weather-proofed material. Once the siding was up, we painted it. Between the built in weather resistance of the T1-11 siding and an occasional refresh of the paint, I'm expecting it to last at least 10 years (and I'm hoping for more like 15-20) before it needs any significant level of repair. Likewise, you could use T1-11 for your siding if you'd like some detail on the sides instead of just flat slabs of plywood.
In any case, some paint, epoxy coating, polyurethane or other protectant will go a long way toward preserving the wood, no matter which product it's applied over.