We have both Hickory and Live Oak trees in our 2 acre lot near Peace River (Florida). The Hickory trees only grow near the river, upland from the river Cypress. The Oaks are uphill from the Hickories, so we are right on the border and have LOTS of squirrels. The squirrels are well fed with both acorns and hickory nuts. The funny thing is that the squirrels will gather hickory nuts from under the hickory trees, but carry them over to the oak trees to eat them. So there are piles of hickory nut shells at the bases of the oak trees. The squirrels also eat acorn, but there are no big hard shells left from that. Both are wonderful shade trees, but both will be damaged by severe hurricanes like we had in 2004.
Those are gorgeous trees, especially with the Spanish moss (I assume) waving in the breeze! They seem to have fared well so far, despite the storms you mentioned.
The oaks in our yard, and I think all of them, retain some of their leaves over the winter giving many critters shelter. Maybe your squirrels have built homes in the oaks, or that's where the fur-family dinner parties are held :-) .
Our squirrels made off with a small portion of hickory nuts while they dried under the carport. When I went out in the mornings, there would be empty shells all over the place. I didn't mind sharing, but I did resent the clean up duty, haha.
Thank you for reading and sharing your story and beautiful photo!