Wind power accounts for about 12% of the electricity generated in Texas. That's not enough to account for the cheap electricity in Texas.
A bigger reason is competition.
Texas is the leader in energy deregulation. There are only 14 states with some form of deregulated electricity, most of them are in the Northeast, where NIMBY attitudes have severely limited producers. OTOH, Texas has lots of oil, coal, nuclear and wind power.
I know for a fact that the Texas nuke plants are just barely profitable. It would make sense to eliminate the unfair advantages given to wind power.