Welcome to outdoor climbing purgatory. Most of the land in the state is private property, so even if there is rock, you can't access it. It's probably limestone anyway around these parts, so trad options are more limited.
BUT since you want trad, then Enchanted Rock, Quartz, and the Wichitas are your friends.
Additional spots within 5 hours drive:
Inks Ranch is open for select weekends and is adjacent to Enchanted Rock. Access Fund has the info: https://www.accessfund.org/inks-ranch
Robber's Cave in Oklahoma has some trad lines.
If you're in far north Dallas suburbs, 5~ hours travel time can put you in Arkansas. Horseshoe Canyon Ranch has 100ish trad routes in addition to the abundance of sport lines. Mount Magazine State Park has 30ish. Sam's Throne has a bunch. There are a few crags up there that might be within your suggested travel radius.
Summer is hot, but the rest of the year can be pretty mild as far as climbing is concerned.