That's true, but Minneapolis, at the opposite end of the climate spectrum, is one of the most bike-friendly places, and bicycle commuting remains strong through the winter.
That's not to say you can't bike for significant parts of the year, but there are definitely days where it wouldn't just be uncomfortable, it would be unsafe, to bike to work in Texas. Add to that that certain cities, like Austin, are also fairly hilly.
That shouldn't restrict you from ever biking though, as seems to be the excuse some people are using.