Why are there no trees in Texas?
A quick google image search reveals that, indeed, Texas has quite lush forests. Remember that the state is extremely large (as compared to the Northeastern states, for example), and encompasses a huge variety of terrain, climates, rainfall amounts, etc. While the stereotypical view of Texas is rugged, dusty terrain:


From: http://texasmountaintrail.blogspot.com/2013/12/big-bend-landscape.html

The eastern part of the state borders Louisiana, and is definitely not dusty and dry:


From: https://www.flickr.com/photos/horwath/2488138213/

Rainfall varies across the state from east to west:


From: http://www.worldatlas.com/webimage/countrys/namerica/usstates/weathermaps/txprecip.htm



There are many different reasons why trees are not very likely to grow in certain regions, and these may vary from place to place. There may not be enough precipitation to support trees that are not adapted to a drier environment, while some species of grass could survive just fine. Temperature changes could be too severe between summer and winter (grasses just go dormant or die during harsh winters, and regrow in the spring). Fire is a big issue, as well - prairies often burn, and while grasses can regrow quite quickly, a tree that doesn't mature for 20 years may not make it between fires. Grasslands also have very deep, tightly-intertwined root networks, with some reaching 15 feet (~5m) or more below the surface:


(Click image for higher-resolution PDF)From: http://www.conservationresearchinstitute.org/educational-offerings.html

Tree species that survive the other challenges may not be able to penetrate deeply enough to adequately take root, sustain itself, and not fall over. Also, speaking of which, grasslands tend to be susceptible to tornadoes as well, and while grasses just bend before the wind, trees get uprooted or break. So, while any one or two of these issues may be overcome by a particular tree species, when added together it translates into a very inhospitable environment for trees.