Yes, but rarely.
The last time it snowed here was last April (a first, I believe), and that was only in the northern part of the Houston area (closer to the Woodlands). It was mixed with sleet.
Before that, Christmas 2004. Had four inches, which was a lot for here. Before that, January 1994.
We've had ice storms that have shut down key roads (like the tollway) for days. January 1997 was one. February 1989 was another.