The first time i heard this i was in minnesota watching a riding lawn mower do a wheelie down a side road then take off down mainstreet. the rider recieved a ticket for speeding. The thought behind this phrase is simple.. mail men get you you're mail usually overnite... from places all over the country, not much is faster then that. hence "hauling the mail"
Man1: a barstool with a 5hp motor on it? This is crazy!
Man2: yeah these things are awesome.
Man1: did you see how fast they were going?
Man2: yeah man, they were "haulin the mail!"