The owner of the wagon is Aeolus, the Greek keeper of the winds.
The wagon is used as a stall to sell bags of wind. The bags of wind cost one drachma. The cost of a refill is free.
Role of Aeolus' Wind Wagon in Mythology Island
Using the drachma that you get, buy one bag of wind. Use it to fly up to Zues' "lair" and defeat him. If you mess up, you can get another bag of wind for free.
The wind will lift you up, and you have to move your mouse around to go and get to Zeus.
To give you wind so you can fly up and defeat Zues.