The full wood stock served a number of purposes. They protected the soldier's hands from barrel heat. And yes, this was even the case when they fought with muzzle loading muskets. After 5-10 minutes of continuous fire, the barrels would get too hot to touch. Not a problem for firing, because of the bottom wood. But definitely a problem for reloading. During the heat of battle the British infantry were known to use their sling as a sort of pad to protect their hand while reloading. But there was always the risk of a cartridge catching fire ("cooking off") during this process. If things got really bad, soldiers would pour water, or even piss down their barrels to cool them, and to clean some of the fouling. Then if they needed to keep firing they would pour in the powder from a cartridge, leave it unrammed, and touch it off to dry the barrel.
But back to the topic at hand. The wood also kept at least some of the mud and water off the barrel. On some rifles they served as the anchor point for the bayonet, so as not to affect the way the rifle shot depending on whether bayonets were fixed or not. They also often served a purpose in barrel bedding, or (as in the case of the SMLE) to place upward tension on the barrel. And sometimes they even housed parts of a rifle's mechanism (eg: the upper handguard on an SKS).
But I think the main reason is that it looks badass.