Not Legal Advice:
No. A Youtube video from ComedyDriving.com even encourages you to go bare, as it's not illegal to drive barefoot in Texas.
ComedyDriving.com is an online course brought to you by professional comedians, with years of entertainment experience. This course was designed from the ground up to be both educational and enjoyable. For more information you can visit them at: www.comedydriving.com.
This question also pops up from time to time on FindLaw Answers traffic law forum, and may be on drivers’ minds as summer approaches.
The short answer is no: There are no federal or state laws that prohibit driving a car without shoes. But state laws may be different for other types of motor vehicles like motorcycles. And local jurisdictions may also put their foot down when it comes to driving barefoot.
Get more info about barefoot driving here: blogs.findlaw.com.
Refer to Texas Driver Handbook, explaining applicable federal and state laws you need to understand in order to successfully operate a motor vehicle in Texas.