Best Natural Building Style For Kentucky

I'd like to try building a structure in the woods on my property with my son, who is 8.  We want it to be an all natural, long lasting, playhouse for him and his sister to hang out in.  It's in the woods under a canopy, but it definitely still gets a decent amount of rain in there when it comes down hard.  So I need to make sure it's water-proof, or at least water resistant so that it doesn't fall apart when wet.

Most specifically, I want it to be something I can build with the wood and dirt and anything else found locally here in Kentucky.  I don't mind buying some straw bales, for instance, but I'm not looking to spend significant money on 2x4's and shingles.  Ya'll know what I mean, or you wouldn't be on this forum.  

Any advice is appreciated. Once I know the best material/style to look at, I can do a lot more research.

Thanks!

To my mind, the roof is the only part that is problematic. If you don't want to buy shingles or other roofing, you have three choices that I can think of: learn to split shakes (probably beyond an 8 year old's strength); use local clay if you have it to make tiles which you fire in a home-built kiln (a stretch for most people's skill and reasonable effort unless you are a potter); or strip bark from trees for shingling, on a steep roof slope (I think this was a method pioneers in your region used for initial shelters). If you have a lot of slate or flat thin stone in your area, you might be able to use that.

Otherwise, I might use a mix of techniques, including some stone wall base, roundwood framing, cob for parts of outside wall, maybe partly log cabin... it really depends on the character of your particular resource mix. If doing any amount of cob, I would frame up a roof first so it could be worked on under shelter and be usable before full completion.

Traditional vernacular for Kentucky, in the popular imagination at least, is the log cabin. I recall my father building the lower half of one in the woods near our house when I was around that age, and I may have helped sawing notches and such. You could make a gappy structure which would be simple and forgiving, and chink it with cob. I now have a nine year old grandson who is interested in doing such things though not very able yet.