You have a beautiful piece of property. We had a four board fence very similar to yours constructed on our property last April. Our fence is 5 foot tall and I, too, needed to plant some shrub/trees that would provide some privacy. I already had some shrubs planted prior to the fence and they, of course, have stayed. Loropetelum, variegated privet, and wax myrtle. I plan to add one or two cestrums in the shady areas along the remaining fence line.

Molly

Some other suggestions might be cherry laurel, eleagnus Russian olive, cleyera japonica, hollies, viburnum.
Also see:

Aggie Horticulture: Large Shrubs for Texas

Oleander hedges are absolutely beautiful, especially when in bloom but the foliage is a lovely dark green. I had not seen them used that way before, but here in the North Houston area I have been seeing lots of them. Some are trimmed like a standard box type and others are left to go tall. I was recently driving by a large building might have been a bank and saw one that looked very similar to this one. I actually stopped and went to look at it to make sure it was Oleander. To see some good pictures go do a Google Image search for Oleander hedge.

Oleander · More Info

Makes me want one!

Beautiful place you have.

+1 on the Oleander. They won't require much water at all. Very dense and pretty.

There is an edible guava that is cold hardy and also the flowers are very nice.

Yes, pineapple guava (Feijoa Sellowiana) is an excellent, evergreen, sun loving shrub with beautiful flowers and bears small, olive size fruit. I planted 3 of them along my fence and I really like them. They can get quite large, but respond well to occasional pruning.

Molly

Thank you Molly. My mind was frozen and not popping with the appropriate name and I was too lazy to go google.

I think an occasional structure with a vine would be really cool. I love Banksai rose used that way. It will get very large and gorgious.

Should take a look at what Aegis1000 has done in this current thread on the GW landscape design forum; would have to switch much to Texas adapted plants, but the general design ideas for privacy are pretty impressive:
Show me your small private backyard landscaping

Never knew of a person or pet falling ill from the beautiful oleander hedges that lined several of the bayous in southwest Houston even though all parts of this plant are somewhat poisonous. Not likely to be an issue unless you expect to have herbivores or raise honey bees on the property, but still something to be aware of.

Oleander poisoning

Sounds like you made some great choices.

Don't know why I didn't think to recommend bottlebrush, I have some in a section of hedgerow. With plenty of water and fertilizer, they can grow pretty quickly, although the wood can tend to be weak/brittle. Their best feature, however, is the hummingbirds that their blooms attract. They absolutely _love_ them so be sure not to miss the show. :)

Our kids' dogs occasionally chew on the acorns that blanket our neighborhood and contain toxic gallotannins (yes, oaks are on the poisonous plant list). Various parts of our dwarf peach trees, Texas mountain laurel, groundsel, asclepias, baptisia, and I'm sure others we are not even aware of are also toxic to varying degrees. Pets rarely consume enough (if any at all) to make them sick, but is good to be aware should they ever show symptoms... and to educate kids. With awareness, don't know that oleander would be significantly more dangerous than these others, but does merit some special consideration as "probably the most toxic plant in Texas" (AgriLIFE). TAMU Extension maintains a good list of toxic plants for the livestock folks on Plants of Texas Rangelands.

Strange about oaks, because I heard that one could make flour out of live oaks.

Can make flour, but believe the tannins must be leached out first or else bitter and toxic. The process and potential for kidney damage if skipped is mentioned on Eat the Weeds: Acorns on Eat the Weeds

Interesting that both ETW and TAMU sites indicate that live oak acorns tend to be less toxic than others.