I chop when I dig a bald cypress, whether it is December, January, February, but not March. I don't dig in March. There's snakes in March, and April, and May... Water moccasins an copperheads. No.
We don't usually get below the upper 20s after the end of January. If I had a potted tree growing HEALTHY AND STRONG THE PREVIOUS YEAR, I could chop it at the end of January. If you want to chop a tree, watch the buds every day. If they start to swell before the end of January, chop then. If not, first week of February is about the latest I'd wait. We get nights in the low 30s and days in 40s and 50s in February (see note below). That's when the buds seem to really push, but some trees wait until March (to spite me and drive up my blood pressure). If the tree is potted, leave the roots alone. None of my trees are in the ground, so my uneducated advice for in-ground BCs is to treat it like a swamp dig, chop the trunk, remove all remaining branches to the trunk, and cut the roots to potting depth.
Shit, one more thing. Besides only chopping trees that were healthy and strong the previous year, THE TREE CAN NOT HAVE BEEN DUG AND POTTED THE PREVIOUS YEAR. The trees need their rest after being dug. That's why, when I dig, I cut for the root depth for my black mason tubs, and I chop to a height a few inches above my estimated target height. I get it all done in one shot. Digging a BC, like most all trees, is a very stressful event. Doing a chop the very next Winter robs the tree of all the effort it took to get those first-year shoots growing. Then you have a very weak (or dying) tree.
Improvisational potting:
Christmas tree watering pots. They're typically green wide, and only a few inches deep. I "liberated" some pots from a vacant lot in March. They were left by a Christmas tree company. You could buy your own, but they're sold by the 1000-lot size.
Restaurant bus tubs. They come in 5, 7, and 9-inch depths. I like the 9-inch depth, but I only pot 5 inches deep, and fill the rest with water. Always keep small bottles of insecticidal oil nearby to keep mosquitoes from growing.
Medium mason/mortar/mixing tubs. Find them for under $6 at local home improvement/construction supply stores in the concrete department. Roughly 20x26x7 LxWxD and 10-gallons in size.
Large mixing tubs, 2 types: There are two types of large mixing tubs, and the same store will change their supplier on a whim. The first is roughly the same length and width as the medium tub, but it is much deeper. I only recommend this if you are potting to 6-inches deep and flooding the rest for root-swelling. The other type of tub is only 7-9 inches deep, but 24x36 long and wide. This is good for big big big trees (and $800 bonsai pots).
Note on New Orleans Winters: We live between the warm gulf an the cold continent. Sometimes the two clash and compress the air as they do. That's how we can have days in the 80s during the Winter. I only mention that to show that everything I say is relative to life here in the South. Houston and Mobile are in the same situation. Just 100 miles north of here, and my advice may mean nothing. That's why I'm trying to explain WHY I choose a particular month, and not just WHEN.