In the case of a protracted siege with no hope of relief, the forest would, as you suggested, provide raw materials for the attacking side. One of the most successful medieval siege engines was the trebuchet. It’s main advantage was that it was never transported, it was always built on site. An abundance of wood would (see what I did there?) allow the besiegers to construct trebuchets to launch heavy rocks, fireballs, and dead farm animals over (and at) the walls. To be honest, the only situation in which I can think that a forest could benefit the attackers is in escaping or foraging. A small enough group could, if sufficiently skilled (or lucky) be able to pass unobserved through the forest. Such an escapade might be nigh on impossible on open ground, particularly with a well laid out siege.

The only possible situation in which a forest could conceivably be a significant advantage for the defenders is if they cleared out parts of it first in order to funnel the attacking army into ‘death zones’. I believe the French employed this with specially crafted triangular walls in front of their castle entrances - the word for these particular defences eludes me at the moment, and a quick search for castle funnel exhibited an extensive number of ferry companies. I digress. If the enemy soldiers could conceivably be funnelled by the trees into particular areas by the castle walls, one could see how the defenders could turn the presence of the forest to somewhat of an advantage.