Since it's impossible to leave a completed dungeon without picking up the heart container dropped by the boss, you obviously can't do a three-heart run or anything, but... I've done a run where I've 100% everything except tunic/sword/shield upgrades and...yeah. The rest of the game is a nice challenge, but it's not impossible or anything. Just takes skill and quick wits and whatnot. There isn't much I have to say about super risky environments except to not be clumsy. xP So, a playthrough with the green jerkin isn't much different than a standard playthrough, really. It's just annoying at times. The sword is the same way, though. You just have to strike things more times because it does less damage. So yeah... mostly the same.
The final battle with Ganon? ...Not so much. With the green jerkin, the impact it has on your life meter is outrageous compared to anything else in the game. These are your heart depletion factors:
Contact with Ganon - 8 hearts
Contact with Trident - 4 hearts
Contact with fire - 4 hearts
Also, attacks from the Master Sword cannot harm Ganon unless you perform a spin attack. Even so, these attacks do minimal damage making you have to strike him, like, 12 times before he even starts channeling fire. Charging spin attacks slows your walking speed and makes you pretty vulnerable to attacks. This makes it really difficult to avoid getting hit if you don't know what you're doing--and because the green jerkin is so penetrable, merely a few slip ups can lead to a game over.
So... Carbon. I bid thee luck.