Who gave Hermes his winged shoes?
Zeus did that. Hermes was the son of Zeus, but he grew up very quickly and one day he decided to seek out adventure. The first thing he thought of was to steal Apollon's oxes and he actually did that. Apollon didn't know who it was at first, but he soon found out that Hermes stole the oxes and took Hermes to Olympus on trial. Hermes confessed the crime and made a deal with Zeus which made him the messenger of the gods. After that, Zeus gave Hermes a wand, a round hat and the Sandals.
When Zeus called Hermes to Olympus to chide him for stealing and lying, Hermes promised he would never again lie if Zeus named him as his messenger and herald. Zeus quickly accepted this offer, and told his son that his duties would also include protecting travelers, promoting trade, and negotiating treaties.
To ensure rapid delivery of his messages, Zeus presented Hermes with golden winged sandals as swift as the wind
Is there a text anywhere that this can be pulled from? Having evidence is key in answering these types of questions.
I've added a source which contains exactly the same as my source which was written in Greek.