Yes.... they are legal in Texas. Lots of folks use AR's for hog hunting as well. Of course, as many hogs as there are in Texas, I don't think they'd mind if you used sling shots and air rifles to shoot them. They are a nuisance of the first order.
The trend lately is to use the improved cartridges to shoot heavier bullets.. in the 75-80gr range. That would drastically improve the performance of the .22's on deer sized game. The ballistic co-efficient of a heavy bullet like that would ensure very good penetration.