Oakleaf hydrangeas, once established in 1-3 years might do best but I hesitate recommending them because they WILL still need about 1" of water or rain weekly during the growing season and some moisture every two weeks or so during the winter.

Competition from tree roots that "suck up most of the available moisture" would be very bad. And blockage of rain by the tree canopy would not be good either. It would depend on you for moisture.

I guess it all depends on how 'dry' things will be. If too dry, nix the idea and perhaps consider a potted hydrangea... if you can place it in an area where you can provide it with morning sun & moisture on a regular basis.

I have 2 planted at the fence line by oak trees. They struggle. I keep thinking that if I can get them to year 3 they will be fine. But then last winter took one of them. Dryness is brutal because they wilt at the first sign of heat.