First, ask whoever owns the land if you may "rescue" a few small trees. If you don't know who is the owner, your local tax office can ID the person for you.
Second, ID the trees. They may be something you don't want, like chinaberry or hackberry. Your local library probably has a book on Texas trees.
Third, if you do relocate the trees, do so as quickly as possible since trees are going to break dormancy very soon, and it is best to transplant while they are dormant. You will need to keep an eye on them all summer, giving them adequate water. Plan on losing one or two--no fault on your part, it just happens.

The willow tree is the last tree you will want on your property. They take A LOT of water and are messy. They're great along a creek in a natural area, but not on a residential property. I would definitely try to locate a small oak tree out there if there are any. That would be your best bet. A redbud would be nice too if you can find them. They might have flower buds forming right now, but may be small enough to move without any worry. Dig as much width of a rootball as you can, but you don't have to worry about getting it really deep. If the tree is one inch caliper, then try to get about 9-10 inches on either side for a good section of roots. If it is two inch caliper then 18-20 inches on either side and so on. Good luck on rescuing those trees!

I agree with denisew.Willows will take over sewage lines and sprinklers! PJ

Too much sage advice for me....I'll buy something I know about, and take my time. Oak (red, live) seem so popular here in Texas. I have two live oaks in the front yard. I know to avoid poplars. Pecans are intriguing, but messy, although the back fence line is far from the house. Perhaps maples...before we close this, any recommendations on either tress or nurseries. I went to Bob Wells in Lindale for a couple asian pears...liked the people.

We have bought trees and grape vines from Bob Wells Nursery. We trust his judgement and advice. You might want to e-mail him with your requirements and see what he comes up with. In the long run, it might be cheaper, and less stressful to purchase trees, rather than taking a chance on transplants that may or may not be what you want and might not survive the transplanting. Planting trees is a good thing to do, and we wish you luck!

I hate to throw a negative hat into this ring...but, there is oak wilt out and about. Oak wilt seems to love red oaks, from what I have read and seen. And, according to the people at the site below; many oaks are affected by oak wilt (not just the red ones). On the other hand, I sometimes feel compelled to plant oaks of all varieties in the hopes that some of mine will survive and keep going forever. Wishful thinking? Who knows? Just something to consider when deciding about the giants of your landscape.

Here is a link that might be useful: http://texasoakwilt.org/

Some other good choices to consider are:

Sweetgum (FRUITLESS, unless you like big spiny seeds)
Chinese Tallow Tree (though they WILL send up seedlings everywhere)
Shantung Maple (some maples have brittle wood, so be choosy)
Magnolia
Redbud (for small, shady pockets)
Pecan
Fruit trees, if you can handle the extra care

Thanks all for the continued discussion. I did plant several fruit trees (dwarves) in a mixed orchard area of sorts. I think I sense the shared sentiment that trees are a good investment, not just for my yard, but for the planet. Maybe I'll buy a buch of pecan trees from Bob Wells. They were working through truckloads while I was there.

I'm sorry, but I have to respectfully disagree with Mommyfox about the Chinese Tallow tree. They are considered a noxious weed, especially in southeast Texas, where they are crowding out natives, and costing lots and lots of money (our tax dollars, I'm pretty sure) because people are having to go out and attempt to control, if not eradicate them. Please, please, please don't even think about planting Chinese Tallow trees.

The primary oaks affected by Oak Wilt are red oaks and live oaks. Since you already have 2 live oaks, I'd consider other trees. Yes pecans are messy, but so are live oaks, and pecans provide food. Think of the wonderful nut and fruit deserts and snacks you'll get to make with your future bounty. Remember, though, that pecans get very large, so give them space.

Your local nursery, such as the Bob Wells Nursery you mentioned, should have a good selection of trees for your area.

Some other trees to consider are Cedar Elm, Bald Cypress, Bur Oak, Chinkapin Oak (the latter 2 are not as susceptible to oak wilt), Texas Ash, Chinese Pistache, Drummond Maple, Mexican Plum, Golden Raintree, and many more that I bet you find at the local nursery, if it's a good one. Just remember, plant a diverse collection for beauty, for the health of the tree, and especially for the wildlife.

Sally