Ask Mr. Smarty Plants

The insects you're seeing is almost certainly not moths, but butterflies.  Texas is currently experiencing an explosion in the population of American Snout butterflies, Libytheana carinenta.  These population explosions regularly occur when certain climatic conditions are met.  During these times, billions of adult American Snout butterflies - which do resemble moths - may take to the air in Texas.  Other states may see similar flights of this species, but in much smaller numbers.

The good news is that American Snouts do not feed on Live Oak, only hackberry.  In fact, while the caterpillars of this species can, when the leaves are just emerging, feed on the foliage of any hackberry species, they actually feed almost exclusively on Celtis ehrenbergiana (spiny hackberry), listed as Celtis pallida by some sources.  For more on the interesting life history of this butterfly species, see this excellent article on American Snout "migrations."

The adult American Snouts visiting your live oaks are probably attracted to the nectar-like secretions of plant-sucking insects, like aphids, living on your oaks.  Though aphids and other insects like them do take some food and energy from Live Oak trees, they rarely cause enough damage to be of any real concern.  For more information on oak pests, please visit this webpage from the Forest Pests website.