The only advantage they should have (IMO) is range. They do seem a little overpowered in combat effectiveness compared to firearms. Getting hit with an arrow shouldn't have the same impact as getting hit with a bullet, especially if the natives are firing at long range to stay outside the range of muskets. The European units weren't armored, but they did have multi-layer jackets, gloves, boots, etc. that would provide at least a little deflection for an arrow. The Eastern unit (horse archer, can't remember the name) might be a little more realistic, if they were using compound bows that hit harder.
firearms were (I believe) developed because they could easily shred through the armor of heavy knights, which arrows couldn't. This made bows obselete and muskets became mass produced. The problem with this is that when people started using muskets, armor was removed so many used light armor as opposed to heavy chainmail and such.

If I remember correctly from my history class last year, many troops in the American colonies were low on supplies. In the American revolution, the Americans were often walking barefoot and starving. This may not be the case, but arrows could quite easily penetrate fur or cotton (or whatever material was used) uniforms.