It can do fine with just 2 hrs of sun. I have Little Lime in full but bright shade (albeit the more sun it gets, the more blooms it produces). However, "a fair amount of drought and a lot of drying winds' is not a location for which I would recommend hydrangeas.

Well, I've already got some brand new Snow Queen Oakleaf Hydrangea and Ruby Slipper Oakleaf Hydrangea plants in the same area and they're doing great...so far. They didn't even have transplant shock. However, are temps have been cooler than normal and we have been getting a lot more rain than usual. I was told by a fellow gardener that he sees oakleaf hydrangeas all over in the Kansas City, KS area usually planted on the north side of buildings or houses like mine are. And here on Houzz, someone said that their oakleaf hydrangeas thrive in TX, so I figured they should do well here too. Below are photos of two of these plants. I've seen some big leaf type hydrangeas here too and they seem to be doing well. I'm just not sure about the shade and the Hydrangea paniculata though.

Snow Queen Oakleaf Hydrangea

Ruby Slippers Oakleaf Hydrangea

Oakleafs are the most drought-hardy of the hydrangeas but that does not mean they will thrive in dry conditions. If you can provide moisture and protection from the winds you will create a micro-climate in which they can be grown. But I took your statement literally when you said 'We usually get a fair amount of drought and A
LOT of drying wind.' I therefore pictured them being subjected to those conditions and not doing well. If you see them in gardens in your neighborhood then I would take that as a 'yes, they can be grown'. Maintain the soil as evenly moist as you can, keep the mulch between 3-4" year around and do not let them sit in poodles of water.

I have
a water faucet on that side of my house right where they are growing,
so giving them plenty of moister won't be a problem. I had
hostas over there before and they thrived, although the hostas did suffer
from leaf scorch later in the summer, possibly because of the heat and wind
combo.

I also have the oakleafs
mulched with about 3-4" of pine needle mulch, which greatly helps retain
moisture in the soil. The soil is always
moist, but not soggy.

Oakleafs will THRIVE in bright shade sheltered from wind. In fact, I will be moving a beaten-up Alice off of a wind-swept north facing slope to a location that's sheltered from the south, east, and north that gets 2 hours of direct sun per day. Oakleafs of dark foliage color (from not being in the sun all day) look awesome, especially when contrasted with the white blooms.