Under the Texas Penal Code, a person commits the offense of driving while intoxicated if they operate a motor vehicle after having lost the normal use of their mental or physical faculties due to the consumption of alcohol, a drug, or some combination of the two. A motor vehicle is "a device in, on or by which a person of property is or may be transported or drawn on a highway..."
So, in the Lone Star State it's acceptable to get hammered and pedal down the road on your bike. You might have a hard time keeping your balance, but at least you can't get tagged with a DWI charge.
But try doing that in Louisiana and it's a different story. According to this story from Shreveport's KTBS, Robert Earl Batton found out that Louisiana truly is in a different world as he managed to get arrested for driving while intoxicated while riding his bike. According to the Section 14.98 of the Louisiana Code, operating any means of conveyance while intoxicated is a crime.
So just remember the next time you're down in the Big Easy that you can walk around the French Quarter and get as liquored up as you wish -- just don't get on a bicycle afterward.