In one room with a spinning fire, you can avoid changing the switch to red by using a bomb boost to get around the switch wall.
If you enter Misery Mire first, and obtain the Cane of Somaria, you can skip all the backtracking in Ice Palace. This is a method used if you are unable to get the bomb boost. It is slower than the bomb boost. Instead of pushing the block from the upper floor, just use the cane and put the block on the switch.