Ask Mr. Smarty Plants

Mexican heather, Cuphea hyssopifolia, does not appear in our Native Plant Database because it is native extending from Mexico south to Guatemala. There is more information on the Floridata site linked above. Mexican heather is hardy in USDA Hardiness Zones 9 to 11. Austin is considered to be in Zones 8a to 8b. It can be brought in and grown indoors, but it needs to be done slowly, permitting it to accommodate itself to the extreme indoor climactic conditions. Ordinarily, outside the hardiness zones in which it can thrive, Cuphea hyssopifolia is considered an annual. It would probably have a better chance of surviving outside if it were planted in the ground, rather than a pot. Freezing of the roots is fatal to any plant, and there is a lot less insulation to the roots in a pot, rather than down in the warmer dirt. We wouldn't recommend taking it in and out, but slowly acclimating it to being indoors the rest of the winter. Pictures of Mexican heather.

There are three hydrangeas native to North America: Hydrangea arborescens (wild hydrangea), Decumaria barbara (woodvamp), and Hydrangea quercifolia (oakleaf hydrangea). None are native to Texas, but more so the southeastern United States. The most popular hydrangea in the U.S. is Hydrangea macrophylla, a Japanese native which is hardy to USDA cold-hardiness Zone 6.  Again, it would be better protected in the ground than in a pot, or you could move it gradually indoors as you do the Mexican heather. Pictures of Hydrangea macrophylla.

Finally, Lantana urticoides (West Indian shrubverbena) is a common Texas native. There have been a number of hybridizations of lantana, as well as selections for color of flower, etc. It is hardy to Zone 8, and should survive the winter. However, it will drop leaves and become semi-dormant in cold weather. The branches can be trimmed back, as it flowers on new wood. 

In terms of the plants you are concerned are not looking too good, they all seem to have been recently transplanted, and are probably suffering from transplant shock. The best thing to do now is to trim back 1/4 to 1/3 of the plant, and make sure it is receiving sufficient water. Especially with the pots, you need to make sure there is good drainage so that the roots are not standing in water.  Do not fertilize, you never should fertilize a plant under stress.