What is a safe load in a truck is a package deal - suspension, brakes, frame, tires, wheels, binding/securing of the load, etc - and don't forget the nut behind the wheel. Like a chain, the weakest link is critical. My dad was from the era of sorry tires. He used to insist that you just needed to judge the load against the tires. He was wrong as tires have improved and are not always the weakest link. Even knowing the weakest link is not enough as these individual factors can combine or contribute to create an unsafe load.
I'm sure there are many of us who overload trucks and/or trailers, but the OP never said how much green wood he hauled so give him a break. He spoke in terms of dry wood. Further given the small splits it is probable that a cord of his wood is lighter than an equivalent cord of normal split firewood. The scales will tell. Ron