It's explicitly not a horse. It's a quasi-real creature that by default resembles a horse and uses the statistics of a horse. Those statistics include game-specific attributes such as AC 10, 13 HP, etc. Nowhere in the stat block does it discuss wagon pulling.
It's not a horse. It has a specified speed and the limitation that for the duration it can be ridden by the caster or a chosen creature. That's all.
In any case the OP asked how other DMs would rule it. I've given my answer and my logic. Feel free to rule differently.
