From a previous Mr. Smarty Plants answer:
"We have been receiving many questions regarding what to do after the sudden hard freeze that occurred recently in Central Texas. One thing that applies in every case is, don't fertilize. Plants should be fertilized in the Spring, when you want to encourage new shoots to appear. The last thing you want to do is encourage new shoots now that will put more stress on already-stressed roots.
You may already know what happened; actively growing plants still have water in their upper structure, particularly the leaves. A sudden hard freeze causes that water to expand, bursting cell walls in the leaves, and they quickly turn dark and look pathetic. What made this freeze worse was that it was earlier than we ordinarily expect these conditions in this part of Texas, very sudden, temperatures went down very far, and remained below freezing for several hours. A gradual decrease in temperature over a period of time increases the ability of plants or plant parts to withstand cold temperatures. A sudden decrease in temperature in late fall or early winter usually results in more damage than the same low temperature in January or February.
The information that you found in our database is exactly what we know about the hardiness of the Cordia boissieri (anacahuita). Was your plant protected from those hard, cold winds we had during our cold snap? If so, that might give you a better prognosis. The first thing to do is determine how much of the tree is still alive. Obviously, the leaves, probably black, are going to drop off. On the trunk and branches, use the thumbnail test. Scrape away a very fine, very small layer of the bark, beginning with upper branches and working down toward the base. If there is still some green beneath that scraping, that part of the plant is still alive. If it is black or even slimy beneath the outer bark, that portion of the plant should probably be marked for pruning. The good news is that the bark and woody portions of the tree have stronger cell walls, and are not so apt to burst in freezing.
From Texas A&M AgriLIFE Extension this article Follow Proper Pruning Techniques will give you some good information on what and when to prune. In any case, we would not disturb it except to remove dead areas, and wait to see if it starts to come back in the Spring. Hopefully, the roots were well enough protected by the soil to keep them from freezing, too.
This is an illustration of why the Lady Bird Johnson Wildflower Center recommends the use of plants native not only to North America but to the area in which the plant is being grown. You knew you were gambling to plant the Mexican olive this far north; we hope that you will ultimately win the gamble and retain a live tree."
From our Native Plant Image Gallery: