Does my horse need a shelter?

Yes your horse will require a shelter. The heat in Texas can be horrid. Are there trees for shade on the property? That would help in reference to where maybe you plan to build a shed, but you are going to need one. Have a properly sized pole barn put up and then you can build on it yourselves with time. It is not difficult to put in the walls and doors.. Good luck on your new move and getting to bring your horse home. That is great.