Since Beorn is 'immune to player card effects' does that mean that I can't use (for example) Warden of Healing to heal him?

If I can't I've been playing him wrong for a long time.

Beorn will ignore the effects of all player cards and cannot be chosen for a player card effect such as Warden of Healing. Note that this rule does not effect him when he is not in play, so you can use Fortune or Fate to revive him after Beorn has died.

The relevant section of the rules is on page one, here:

http://www.fantasyflightgames.com/ffg_content/lotr-lcg/support/rulesheets/hobbit_over_hill_and_under_hill_rulesheet.pdf

Oh well, so much for using Beorn in my deck (I've been using him to take massive amounts of damage then healing him).

There is another effect in Tactics that can be used to revive Beorn: Landroval will bring back Beorn as he is defeated with 1 damage. Unfortunately, I think that Tactics and Spirit are the only two spheres with an effect like this for now. I can understand it is less appealing to add Landroval to your deck than Warden of Healing, who serves a more general purpose.

you can also use Dori to target damage on beorn and white tower watchmen.

If Beorn could be healed then he would pretty much be broken now wouldn't he