You need it. Use the foundation guidelines from Abilene as a guide or the basic IBC code. If it's small, like a one car - maybe not. If it's any size at all and you want a stable, long lasting foundation then yes - footer and beams. West Texas has very expansive soils and without a proper foundation, the ground will move your slab around and possibly break it. Been there, had that.
They use those deep footers up nawth because of frost heave issues. We can experience a little that, but it's very rare that we get that cold for any length of time. We really have no "frost line" out here. Usually it might stay below freezing for a couple of days, then it'll be 80. I painted my floor in December and it was about 85 the day I rolled it out.
Also - you do not nail the walls to the slab, you place galvanized 1/2" bolts minimum every 6' , no more than 12" from the corners and bolt the bottom plate down.