Please follow this video for instructions.
Using FMC to consecutively clip ~10 times, it is possible to clip through the Snow Wall, skipping the Firerod completely.
To obtain the Firerod, you must destroy all skulls in this room. Instead of using bombs, you can also simply walk over them to make them shatter.
To get the Links onto the ice platform, cross the room with Green and then reunite. As the Links float over the ice, press X to interrupt the process. Then switch to the Link(s) on the ice and destroy the skulls.
Note: You must be very careful with the movement since falling down most likely results in a very bad, unfinished skull pattern that requires timed bomb throws. For a quick direction change, rolling helps. Ice Physics in this game...
In the room with the ?-Platforms, you can do a Gap Skip to get pass the first gap to the right
The second gap (upwards) must be crossed with a Wall-restricted Gap Skip.
If purple does not make it over, have him grab a pot from the lower-right corner and try the same thing again. If there are no pots left, it is usually best to reset the room. To spawn at the entrance, hold c-right against the bottom wall and fall into the pit. One of the links should spawn back at the entrance.
A consequence from skipping the upgrade is that you have to step on 5 switches at the same time.
This is possible by turning rapidly between two switches.
Using Green for that makes it much easier.
Usually one must cross the room with those colored blocks to get access to the Fairy. However, this room can be entirely skipped by performing this trick on the screen before.
Drop the Links near the ice block at the entrance, then cross the room with Green and position him next to the torch. Reunite with C-Right and then press X as Red is floating over solid ground. You want at least Purple to drop down the pit and respawn at the door to exit the room quicker.
It is not necessary to ever obtain the slingshot here, since you only need it once to hit the switches, and this can be done by doing a jump slash off the moving platform.