Head over to the side of the dragon shaped rock and conduct the wind to blow to the Northeast. Jump off the ice and use the deku leaf to glide over to the final ice platform before entering the dragon's mouth. This completely skips all of the skating on the ice you would otherwise have to do.
Head over to the Eastern side of Ice Ring Isle and melt the ice around the chest. Open the chest to get the Treasure Chart and get on the lid of the chest. The easiest way to do this is to use a jump attack. Now jump from the chest to grab the ice platform and continue on your way to the entrance of the island.
Once you are inside the island. You will notice a wind gust on your left trying to prevent you from getting to the iron boots chest. Instead of taking the route around the wind, angle yourself and roll through the wind to get to the chest.