Ok, Storm Raven, time for some rather severe number-crunching...
The barbarian grappler:
First of all, remember even if the barbarian wins initiative, he only has a 60.6% of starting the grapple (inflicting an incidental 7 hps).
Now let's see what happens in the grapple. The barbarian wins 63.8% of the grapple checks, so each attack nets him 0.638 'succesful' grapples. Thus, to pin the archer, he takes 1.57 attacks. His remaining 2.43 attacks/round he continues to presumably make grapple checks, of which (2.43 x 0.638) 1.55 attacks are successful. Each successful attack deals an average 7 points of damage, so the barbarian can deal 10.85 damage per round for the first four rounds if they are grappling to begin with. If the archer is pinned to begin with, he can do 17.864 damage. If they are not grappling, the best the barbarian is restart the grappling, inflicting an incidental average 4.24 damage, then using attacks to pin, then using a final 1.43 attacks to deal damage. This technique will do about 10.6 damage total. The archer, it is assumed, for these four rounds, tries to escape the grapple, for which he needs to win at least two grapple checks. He has a 29.2% chance of winning two (or more), a 44% of winning one, and a 26.8% chance of not winning any. Based on this, and the numbers above, the barbarian can inflict an average 12.6 damage per round. The archer's best bet is to escape and pray that all of the barbarian's attempt to grappling again fail. Since the barb is hasted- that's pretty unlikely: only 1.7%.
This continues for four rounds, until the barbarian's haste runs out.
It then becomes a different ball-park. The archer, incidentally, is on 50hps. Going into the sixth round, with the barbarian's haste expiring, the barbarian's tactics are still best pinning the archer, since the danger is that he gets out and uses his bow. However, with only three attacks now, he average damage/round is now just 6.39 if grappling, 13.4 if pinning and 6.14 if not grappling. Average damage: 8.17 per round.
However, the archer can now come into play. If he escapes, and the barbarian fails to grapple (10.6%) he can launch his full barrage of arrows, with 3.8 attacks hitting for 37.5 damage (total 142.5). So the archer can inflict an average (0.106 x 142.5) 15.1 damage per round- i.e. more than the barbarian. After two rounds of this, the archer is on 34 points and the barb 77hps (when his rage expires).
Now, the tables begin to turn. With his rage expired, the grapple checks are 50/50. His damage drops to 1.8 if grappling, 6 if pinning and just 1.6 if not. Moreover, the archer's chances are 50% of escaping, 37.5% of breaking the pin and just 12.5% of remaining in the pin. The barb's average damage is therefore 2.225. When the archer reaches 8.9 hit points or less, the barb can change to his greataxe and end it there are then, but this will take another 11.2 rounds. The archer, meanwhile, is still using the escape from grapple, hope the barb cannot restart, and shoot tactic. His chance of escaping are 50%, and the barb has only a 47.5% chance to restart it, so the archer has a 26.25% chance of being able to act. With his 142.5 damage if he can act, he can deal an average 37.4 damage per round- or enough to kill the barb in three rounds.
Conclusion: Archer wins.
Frost Worm:
Okay, so the frost worm will go trill/breath weapon if it wins initiative (22.75%). The archer has a 20% chance to fail (not 25%, as a 5 saves). He will then take the full 52.5 damage from the breath weapon. With the archer stunned, the frost worm can attack him, hitting on 2s or better, so it can do an average 22.325 damage per round. If he isn't stunned, it can do 18 damage. In other words, the archer will die if he fails at least three times (since the frost worm can kill him in four rounds- even with death throes in can only do 99.8 damage in three rounds, and he needs two). Incidentally, there are no AoOs as the archer is an OotBI (forgot that in the original draft!). The chances of failing three times are 0.008, or 0.8%.
So you're right. I should rectify the archer's chance against the frost worm from 100% to 99.8%. My mistake

.
However, this number is meaningless unless you make your character build and then see how he fares.
Edit: Corrected some of the stats.
Edit: Clarified that frost worm can only use trill/BW if wins initiative (since otherwise it is dead).