Your last ability opens with a [i] and ends with a [/b]. Doesn't work too well.
Cold Rage is neat, but almost strictly weaker than Rage. Boost the stat boost, and bear in mind that that's enough because standard rage boosts its own duration.
Mighty Arrow is nice, but nothing to write home about.
Piercing Arrow is scary. Really scary. Touch ACs tend to be so much lower than regular ACs, that I'm going to have to say that's probably overpowered for 11th level.
Storm of Arrows is good, but not incredibly so. A nice option to have, and takes care of mooks like there's no tomorrow.
Perfect Shot/Furious Arrow (change either the table or the ability) is also incredible. If you hit their Touch AC, then you get to make a Concentration check against their full AC to threaten a crit (against their Touch AC no less!). I'm calling this one too much for 13th level, too.
And this is all assuming a 'clean' entry (that is, no shenanigans). Your entry criteria need cleaning up, because I can enter this class at level 2. Human Barbarian 1 with one flaw, Human feat is Point Blank Shot, level 1 feat is Rapid Shot, and the feat from the flaw is Extra Rage. I now get to make all bow attacks as touch attacks, starting at level 4.
In summary: nerf Piercing Arrow, and possibly the capstone. Tighten up your entry requirements. And boost Cold Rage.