fifthwheeleroldman inspires me to respond. I will be 85 in October and ALL of it in East Texas except for years of study and months of travel.
I think Spring is a great time to visit Texas. Here in East Texas we have the beautiful azaleas, daffodils, and wildflowers; great lakeside campgrounds such as Caddo Lake State Park, Tyler State Park, COE parks on Lake 'o The Pines. April would be ideal.
And then one could move on down to the Hill Country around Fredericksburg, Kerrville, with a visit to San Antonio. The wildflowers down there are different than those "up here" in East Texas. We have to admit that the Texas Bluebonnets greatly prefer the Hill Country.
One could start even earlier out in the Big Bend country.
To sum it up: the answer to your question is Spring or Fall would be the best time to visit Texas. Summer? only with two air conditioners and a place to park in the shade. Winter? in THE Valley--lower Rio Grande Valley.