This seems like a fairly substantial change that would have a pretty dramatic effect on game balance. Consider that this grants elves resistance to wooden weapons like clubs and quarterstaves as well as natural weapons. Also bear in mind that it isn't just animals that use teeth, claws, and fists - you're also talking about elementals, some angels or demons, aberrations, and a lot of other creatures. I would say that you're potentially halving the damage that elves would take from a pretty significant number of enemies.
Now, obviously you can mitigate that effect quite substantially if you're planning out all of the encounters yourself by ensuring that your elf PCs very rarely encounter enemies who don't wield steel weapons. Consider, though, that if the rule change has a very limited effect on gameplay it might also fail to generate the flavor that you're looking for.
One way that you might be able to generate the desired flavor without having much of an effect on gameplay is if the elves themselves use primarily wooden weapons to avoid having them turned against them. In other words, most people know that they need to carry metal weapons to overcome the natural resistance that elves possess, and magical beasts like dragons or demons automatically penetrate that resistance, but the elves themselves use primarily wooden arrows as a way of minimizing the damage from friendly fire, or wooden quarterstaves in case they're disarmed or otherwise have their weapons stolen.