Over the years, I have found that near the end of January and early February, the Hill Country usually gets about a week of really nice weather, like clear and in the 60s/70s during the day. Then it usually gets colder again until late March and early April. Mid November and December are when many TWT folks head to Terlingua (Big Bend) for a few weeks. In fact, you can ever rent DS bikes out there from November through about early April from
GSMmotorents.
Here in East Texas where I live, it is a complete crap shoot. A few days ago, we were down in the low 40s. Right now, we are in the mid 70s. Rain generally comes with the big sweeping fronts that roll in from the Northwest and shove their way across the state in a day or three. We don't get the random stuff like we do in the late Spring, Summer and Fall. If you can stay loose on when you want to come so that you can check the weather a few days before leaving, you'd probably be able to time it right. Locking in a date far in advance... well... like I said, it's a crap shoot.
Back in December of 2004, I had a guy from Ottawa come down with his new 1200 GS. He wanted to get away from the Great White North for a week and enjoy the "mild" Texas winter to do some riding. I had a whole week worth of riding planned for him, taking him all over Texas. Then it started snowing... all the way down to Brownsville and Harlingen, the very Southern part of Texas!
He ended up just hanging out around here with me. He'd never done much dual sport riding so I took him out and did a few hundred miles of dirt, sand, mud, and gravel. He had such a good time, we did the same route backward the next day!