Central Texas is largely covered with cedar trees and oak groves (in the Hill Country), with large Cypress along the rivers. It can look Savannah-like when landowners clear all of the cedar in these places. Central Texas contains an abundant number pecan trees and other hardwoods, with large bald cypress along rivers. At least too abundant to be considered grassland, especially in populated areas.

Houston and much of the eastern third of Texas is more like Louisiana and other gulf states. this is generally seen from Dallas to the LA border, and all the way down to the gulf itself. Lots of forests, and some swamps. Forests here are mostly pine, mixed with hardwood forests as you go west.

So overall, Central and East Texas consist of landscapes that just don't fit a grassy description. What you're thinking of is the Panhandle, and that's a totally different landscape/climate, and is actually a part of the great plains. The state is so large that it also has desert areas in the far west (though some mountains in these areas have trees).