We were in San Antonio in January for a month several years ago. Our whole trailer and truck was covered with about 1/2 inch of ice. The cold weather lasted for several days. There were two or three more cold days but not with the ice. IMO, don't count on the 60's & 70's up farther North until probably mid Feb or so.
Of course that weather could have been an anomaly but I don't think it was. The weather in the San Antonio area was usually great for most of the Jan- Feb and March was absolutely delightful up in the hill country.
We have been going to Tampa, Florida for the past 15 years except for that one trip to Texas. We enjoyed it so much that we are going again this winter for our last winter time escape from the frozen North. Hope you enjoy your stay as much as we did. :)
Barney