There are two options to get through the woods.
Backing off as soon as the fog moves closer
This is the riskier option of the two and I wouldn't recommend it but It was the method I used before finding out about the 2nd one. You can carefully walk into random directions and try to back off as soon as you see the fog moving closer. It can be tricky but it's certainly not impossible. Memorizing the path you took can also save you some frustration.
Using the torch as a guide
This is definitely the preferred method if you have a torch at hand (you'll find one next to the 2 stationary torches). You might have noticed how the floating embers were "connecting" the torches in the first half of the lost woods. Well here It's the same. You can light your torch and follow the direction of the fire to get through the woods safely.
Keep in mind that you have to stand still if you're unsure since movement will cause the trail to be behind you for most of the time. Also this only works if your torch is lit so make sure you don't accidentally extinguish it by pressing B or climbing a tree.