Original Method Edit

Using the Infinite Sword Glitch and Bomb Hovering you can enter Snowhead without playing the Goron Lullaby. There's 2 Major obstacles that prevent you from walking all the way up. The first is the big slope at the bottom, and the second is the start of the ramp that goes up to the temple entrance. The first goal is to get to the bottom of the slope, which is the easiest part. There's one snowball that you have to dodge or hit with an explosive, and that's the only troublesome part of the beginning. Once at the bottom of the slope(you can only stand on one side, it's obvious since if you're on the wrong side you'll be blown backwards) it takes 18 hovers to reach the top. The hovers are tricky because you can't backflip while the wind is blowing. A good method is to pull a bomb right when the wind starts, that way when it ends you can hover off the bomb, then follow it with 1-2 Chu hovers, then repeat.

Once you're above the slope you have 2 options. The first option is walk towards the bottom of the ramp, and hover to the ramp and go up from there. It's more difficult because theres a snowball that goes through there, and you'll have to dodge extra snowballs on the way up. The second and much better option is to run to the other side of the slope and hover up near the entrance. You must be careful when running past the slope because if the wind blows while you're on it, you'll lose the Infinite Sword Glitch and be blown off. Walk a bit past the Fairy Cave entrance(which is as far as you can go) and line up your hover with the bottom of the ramp. It takes 15 hovers to get up to the ramp, the last backflip puts you through the ramp. Be careful when backflipping onto the ramp, because a snowball goes right over you. You can easily see it because of the clipping though, so just wait until it passes you then go up.

After that there's only a little bit left. Work your way upwards towards the entrance, and there will be one last snowball in your way. You can dodge or hit it with an explosive, then run passed it. For the last little stretch you can either run there as link(which is a little tricky, you have to be quick) or put on the goron mask right when the wind stops and roll in(easier method).

This TAS video shows you how to enter that way.

Instead of the second hover you can use the superslide that's used in the Wrong Warp method, which is faster and saves a lot of explosives.

Fairy Fountain Wrong Warp Edit

This method is a bit quicker than the first method, but much more difficult. You can Wrong Warp from Great Bay or Woodfall to get to Snowhead. As soon as you exit, though, you have about 1 second to activate the Infinite Sword Glitch or you'll be blown off. To do this, as soon as you exit, hold down so you look towards the screen, pull out a bomb, shield drop it, then activate the Infinite Sword Glitch off of it. You have barely enough time to pull it off, but it's worth it if you can do it. After you get the ISG, walk back as far as the wind lets you go, then superslide behind the mountain. You can use 2 explosives to hover onto the ramp which uses a bombchu, or the easier 1 explosive method. Just climb onto the ramp, then activate ISG as soon as you get onto the ramp. After that just dodge the snowballs and work your way to the entrance.

Using pause buffering as you exit the cave makes the ISG many times easier. It's recommended in a single segment run.

It's not known whether it's completely impossible or just super hard to get high enough in the first hover off the ground to not fall back to the ground. If it is possible, that will save lullaby skip time and explosives because you can backwalk while there's no wind then do a single bombchu hover to avoid getting blown then the instant it ends ocarina dive then continue to backwalk.

Hyper Endless Superslide Edit

A TAS only method for sure. Pulling off a HESS in real time is the easy part of this, which is hard enough by itself. Navigating up to snowhead avoiding the snowballs and getting stuck on the edges makes this pretty much impossible on console.

This TAS video shows you how to enter that way.