Archaeological digs have shown that the Normans used fairly modern-style iron horseshoes at the time of the Conquest, and I believe that they go a bit further back. As others have said, horseshoes probably go back as far as the use of horses, it's just that they were made of materials that haven't survived (ie not metal.)
Etruscans were apparently using bronze horseshoes in the fourth century BC:
I have to agree that while the modern horseshoe was not used as far back as 300 BC, protection of the horses' hooves was necessary. Therefore, regardless of the material used, both the modern horseshoe and the early horseshoe had a purpose.
Apparently, really hard (no pun intended) evidence for the use of iron horseshoes doesn't really begin to appear until around 500 A.D., although other evidence suggests that such shoes may have been in use seven hundred years earlier. The later the date, the more likely the evidence. Here are two links that may help:
I don't believe that horseshoes were actually used in 300 BC. At that time, there were people *(even into Roman times) who would put leather "sandals" on their horses' hooves. They did so simply to try to protect their horses hooves from getting damaged when they stepped on rocks. However, the things that we would recognize as horseshoes -- iron, nailed on-- didn't really come around for centuries after the time that you're talking about.