3 week palm ?? The preparation for overwintering most plants is to keep them on the dry side. I would not have thought it would be a problem in Texas.

The trouble is that a three-week-old palm still needs fairly frequent watering to become established. I would give it a light feeding of a fertilizer low in nitrogen, but high in phosphate and potash, to encourage it to harden off. That will also encourage root growth, to help it establish faster, so you can cut back on the water. After the hard frost this last winter in Texas, people are justifiably paranoid about frost--I would also gather materials for protection and be ready to apply them at a moment's notice.