Rosemary? There are prostrate, columnar and "bushy" rosemarys. They are tough, beautiful, the little blue flowers attract bees, and you can eat the shrubbery, too!

How about Hellebores, with the added bonus of flowers in winter. They can take quite a bit of early sun, but would need to be in an area with afternoon shade.
There are some small Azaleas - most are at least semi evergreen and East Texas soils would be great for them.
Texas gold columbine are mostly evergreen in winter.
You didn't say whether you mostly have sun or shade, and my yard is mostly shade so these are what work for me.

I was also going to suggest Hellebores - also called Lenten Rose. Mine are blooming now.

I just bought some dwarf abelia that is only supposed to grow to about 3 feet tall and wide. It is the kind that has pink flowers during the summer.

Thanks, everyone, for the suggestions. My yard consists of mostly sun. I planted 4 Rosemary 'Irene' last fall, but it appears only one has survived the winter and it doesn't look good. I have one Hellebores plant located under an oak tree in one of the very few shaded spots that I have. I planted it about 4 years ago and it has never bloomed although it is alive and well. For someone who spends so much time in the yard, I seem to have a rather brown thumb. I have planted a number of Encore azaleas and they are all doing well, but I don't have any more areas that are suitable for them.

How about dwarf gardenia?

Ducher rose seems to strongly evergreen rose after going through several nights of low-mid teens temperature. Not sure just how big it'd get but you could trim it back every winter. Mine didn't get big enough to be trimmed back. Perhaps, I'll find out by fall. It's 2nd growing season for those roses.

I'm going to look for the dwarf gardenia. Not sure how much cold they can take, but I'll look first. I have one standard size gardenia (August Beauty) that is doing well although, I have killed several others. It seems to be all about location, location, location.

I actually have a Ducher rose that is about 8 years old. It has reached the bottom of our second story before, but I now cut it back pretty severely each year so it doesn't get much taller than 8' in a season. I don't know if it's because it's getting to be an old bush or what, but it's not looking as good as it once did. I'm not sure it likes the severe haircut every year.

Wow... that's big. Hmm....

I recall reading somewhere that China roses aren't too fond of being severely pruned back.

Did you prune it back to like several canes about a foot tall?

Lou, actually on that particular rose, I start out with hedge clippers and cut it back to about 3-4'. Then I go in and hand prune out the dead wood. I'm not great with my roses. In fact, I've been slowly culling them out. I removed all the minis and I'm now removing any rose that takes more effort than it's worth. So far, Ducher gets to stay.