YOu can buy a house from anywhere...you really need to find a mortgage broker in Texas closer to where you are considering to see all of your options. Also, consider the insurance factors if you are looking close to the coast, and flood insurance on the south / Gulf side of Texas..Houston to Brownsville.
I think the only thing is whether this will be your primary residence or not. The interest on the mortgage might be higher if you are getting an investment property.
Just make sure that you have a local real estate pro's help so you get familiar with the area, purchse the house you like and do due diligency to make sure there is no surprises.