I don't find it unusual or even undesirable that a first time player hang back quite a bit over the course of his/her first adventure, or even campaign; both in terms of being a player and what the player does with his/her character. Some people will take their time to acclimate themselves to what is a new environment with complicated rules (both in game and socially); some people are just casual gamers. Through maybe the first full campaign, I wouldn't make any special in-game accommodations for the character, they're going to be absorbing a lot from everyone at the table anyway.
As long as everyone at the table is happy, it's all good. As a new player, you should be checking up on him/her (@Tripsed's point #1) to ensure that they're having fun, and likely addressing questions about the game itself.
In these discussions I'd try to find out what pre-concieved notions they have. Even though they hadn't played before, they still come to the table with some expectations, maybe an idea that character death is an unrecoverable failure, or that the other players will mock them (depending on the group maybe they will, but hopefully friendly) etc. Maybe discussing it will sort it out, maybe just playing through more sessions will change these ideas.
The more obvious thing is that as a new player they'll have gaps in knowledge, but these range over multiple tiers:
- The mechanics of the game itself, which are complex enough,
- How your table plays those rules, esp. which aspects you emphasize and which you don't emphasize,
- How to do "theater of the mind"
- The social dynamic at your table,
- The milleu of your campaign, e.g. how the character fits in to the world, and even
- What sword & sorcery fantasy is all about (this can happen if they're not already a fan of the genre)
uncertainty on any of these levels (and others not listed) can lead the player to tend towards trying to play it safe.
As a final note, I wouldn't get too down on the idea of a cautious (wise? intelligent?) barbarian, there might be fun directions in terms of role playing that you could go with this -- turning the table on people who underestimate him/her, or just emphasizing the contrast between his/her normal behavior and what happens when he/she does get angered (say).
TL;DR In the short stories, Conan, the quintessential barbarian, was in many cases a very cautious character.
I distinctly remember the setup of one of the Conan stories. Conan had been assigned to lead a military unit in a war against Koth. He had heard rumors that the Koth army had a sorcerer with them, but knew that "sorcerer's magic was much more effective on the defense than the offense". His side was setup in a defensive position, as the Kothian army approached. He held his troops in position, despite obvious gaps in the enemy's formation, but another commander saw an opening and charged. The ground burst into flames under the galloping calvary decimating them. From there, the Kothians took the field and Conan had to flee, alone (and get into another adventure...).