You can get on top of and even get around the ice cavern without going through it. Follow the right path that goes over the bridge, and instead of going around the left bend, cut right hard and get up over the ice patch to the right. Then, cut hard to the left and follow the path farther up the mountain, being careful not to go too far to the right or left. Once at the top, go right then hug the mountainside using the ridges to keep you from sliding all the way down. You can keep going and skip the ice cavern, or you can go off one of the ridges and land on top of the cavern.