No medium armor? Hide is out of the picture?
The animal companion ability should specify that it levels as a druid's companion as well. Otherwise, no one will want it until they're a much higher level.
Arctic/Desert adaptation--I think when you were outlining energy resistance, you meant to say fire, not heat/flame.
Does catfall stack with Tumble's ability to reduce falling damage (I imagine it does)?
Climb like a monkey is an extraordinary ability. I see nothing supernatural about it.
Discern north has limited uses, but it's an option. I'd recommend adding something after, "This ability lasts 24 hours, and is always active." I would say, "This ability lasts 24 hours, and is constantly active during that time, regardless of antimagic effects (such as an antimagic field).
Healthy as a horse is mostly weak, but I suppose if you didn't have anything else to pick...
Hide from notice is a nice one for a scouting beast warrior. Very nice. I don't see anything supernatural about it though. The color change isn't really supernatural, if that's what you were thinking.
Same goes for jump like a rabbit.
Keen-eared is not supernatural...
Move like a cat isn't supernatural.
Natural armor is cool.
Quiet as a mouse, I imagine, is supposed to say Move Silently, not Sneak. Not supernatural.
Serpent blooded is less useful than the disease resistance one, but I suppose if your DM uses a lot of enemies that spit poison or something, it could help.
Sharp-eyed, slippery as an eel, and swim like a fish aren't supernatural. Just extraordinary.
Venom is odd, because it uses Wisdom for its saving throw. Usually, it's Constitution that governs it. Why a beast warrior wouldn't spend two beast points for 2d8 Con damage is beyond me, but whatever. Maybe you should say it costs two extra beast points for +10 on those checks.
Rapid metabolism is a good ability. Nice little thing to have there. The name could use a bit of a revision though.
The 3rd level abilities look fine.
Animal affinity is cool, but at later levels, it'll start to lose its appeal. Maybe you could change the bonus type to competence or insight or something.
Ferocity is cool. Can you keep using it over and over again?
Natural weapon is a nice ability to pick.
Pounce is a must-have.
Speak with animals is...eh. Flavorful.
Close wounds would be fine as an extraordinary ability. I also think it would be fine to just give fast healing.
6th level is okay.
Aquatic adaptation could probably be extraordinary.
It's ability scores, not ability stats. You said the latter in beast form I.
Circle the herd is a good ally-friendly ability. I like it. Pretty cool. Extraordinary ability, probably, though. Don't capitalize attack of opportunity, and don't put it in quotes.
Reword that under larger than life. Also, this is probably extraordinary, not supernatural.manifest this power as a swift action.
Rend is fine.
Spines is cool, although I would rule that the spines can grow through hide armor. Not that they're proficient...
Holy crap. Sprint can be like overland flight. Except faster. Fast movement x 5 = +50 feet. Assuming human (30 feet), you have an 80 foot speed now. Run gives you x4. 320 feet. Sprint gives x10. 3200 feet. Unless they don't stack, and you're going with the stacking multipliers rule. In which case, it would maybe be something like...80*13 = 1040 feet. Still really fast. I like it, but maybe you should specify if it stacks with the run full-round action, and if it does, does it multiply by 4 then 10, or does it just multiply by 4 and 10 put together with D&D rules (I'm not sure what that comes out to...13 or 14)?
Wolfpack tactics is considerably weaker than circle the herd. I'd say give +4 to already flanking allies, and +2 to not-flanking. Then make it 2 beast points to give all allies an attack of opportunity against the enemy, or make circle the herd take 4 to give that, if you want them to be balanced to each other. You should.
Extra natural attack is a must if you're going with strengthening your natural attacks (you will if you take this class).
Just look above for beast form I's critique. That applies here.
Blindsense already has a radius...
Flight is always good to have, but this might be coming a bit late. Consider moving flight down to a lower level (say, level 7 or 10...a little after the wizard/sorcerer get fly, since flight is potentially more powerful).
Improved extra natural attack should require extra natural attack.
Blindsight already has a radius.
Hide in plain sight is cool.
I think you should provide at least three level 20 abilities to choose from. That way, you can't get all the most powerful abilities of the class, and it makes customization more viable. The class, right now, is railroading players into going a full natural attack route. Maybe you could provide aspects of nature's creatures as choices. Ferocity could be the current level 20 ability. Repose (or something) could be automatic stabilization when dying, in addition to slow healing. It could also improve on the fast healing granted by the previous close wounds.
That's all I've got for now. Feel free to ask questions or justify your supernatural abilities.
Also consider changing the skills per level to 4 + Int mod.