The Druids often state that they're the first ones to take advantage of horse shoeing around 400-500 BCE. However, there lacks enough archaeological evidence to support this. I wouldn't be surprised if it's true, regardless.
On the west side of Italy laid a civilization known as the Etruscans. This link contains some evidence (and pretty pictures) from a tomb around 400 BCE with the following description: "The horseshoes, which are semicircular in shape, are of bronze, and covered a little more than half the foot. Their dimensions are as follows: Nos. 1 and 2, shown in the upper half of the plate, are each 0.125 m broad, and their height when standing on their two ends is in each case 0.097 m. These were presumably the shoes of the two front feet of the horse. The shoes shown in the lower half of the plate are a p399little smaller. No. 3 (to the left) is 0.120 m broad, and No. 4 (to the right), 0.121 m. Their height, when measured as above, is in each case 0.093 m. These seem to have been the shoes of the hind feet. The thickness of all the shoes is 0.004 m."
This Article supports it as well.
Iron horse shoes weren't used until about 500 CE. The only evidence I can find here is regarding the last name of Mariskalk, or horseshoer. The Koran (or Qur'an), written shortly after 600 depending on who you ask, also notes of war horses who, when they walked, sounded like iron hitting stone. This leads us to believe that they most likely wore iron-made horseshoes as well, supporting the the possibility of iron horseshoes first getting used around 500 CE.