In Texas, it is an offense to operate a motor vehicle, in a public place, while intoxicated. A motor vehicle is any self propelled vehicle. One can argue that operating a lawn mower, in a public place, while intoxicated, is not as dangerous as riding a horse, in a public place, while intoxicated,
but any legislature is forced to write broad laws, that sometimes seem to do too much, or too little. In any event, while a professional drunk is unlikely to runover and kill someone on his lawnmower, he is very likely to cause someone to wreck while taking evasive action to avoid him.
I actually saw a drunk farmer run off the road and tear the front wheels off his tractor in ditch. This is when I found out it was legal at the time.