My concern is that the wood could crumble under the load at the hinge on one side if it's too thin, so you'd loose the tree side way.
You can bore cut vertically just at the place you want the notch's apex, as for a box cut. You get the thickness and the quality of the wood. Then an other vertical bore cut at the back of the hinge to be sure. If the front one is good but not the back one, say the front is the back and bore an other one more in front, putting the intended hinge in a sounder wood.
It's quick to do, you get a good idea of the wood, without compromising the tree's stability, well, not really more than it is actually.