I wouldn't worry about it. We had a ton of ice here in ATL during snowpacolypse and as long as you didn't do anything stupid on the hills, I was fine with my BFG MTs. All of my yankee friends tell me that the BFG MT is absolutely horrible on snow and ice. I was cruising around in 2WD most of the time. 4WD for the hill starts. Then again I was screwing around, doing all kinda dumb stuff in front of the Weather Channel news crews so they can show the rest of the US a 40 year old truck doing a bootleggers turn on national TV.
Once you see the pavement completely covered, switch into 4WD. Also keep your speed down. Texas is usually pretty flat so that helps out a lot. Just keep your momentum and don't stop going up a hill. Never let your tank get below 1/2. If you do get stuck, you have a lot more options when you have 1/2 a tank of fuel. Also many times you'll run into traffic jams. I've heard of blowing a 1/4 tank up north just sitting there, idling in traffic. Still better than freezing your rear end off.
Throw a couple meals, some blankets, a deck of cards, and some other misc items to keep warm if you do have any issues. I've got a backpack in my trunk for such emergencies. Something like a jetboil would also be good. Bring some hot chocolate/coffee/tea so you can have a warm cup while you sit in the snow. Also gives you something to do. For being super cheap, get a couple forks/spoons from Wendys then go to the grocery store and get a bunch of cans of pasta. Cheap food that you can eat cold...that you probably won't use anyway.
xWhatever on adding weight. If you can add 500 lbs to the back of your truck, you'll be golden. The best I've seen was a nice thick piece of plate. It was left on a job site and the guy had his buddy lift it in there with a piece of equipment. Avoid bricks as they bounce around. I've seen them bounce around and tear up a drop in bead liner. I guess if you could contain and tie them down then they would be fine. On top of that, get you a bag of cat litter. You can throw that under the tires to give you traction (or so says the TV commercial). Best part about that is that whatever you don't use, give the rest of the bag to your local cat owner, so it isn't taking up space in your garage.