Around Christmas time the question came up whether pine trees are safe to eat for rabbits. Obviously Christmas trees are questionable because you cannot know if they were treated so it is best not to let your rabbit nibble at them. The pine sap is quite strong and has concentrated phenols in it which may be irritating to a rabbit’s mouth (apart from sticking to everything, LOL) Therefore I would stay away from offering parts of the trunk where the bark oozes lots of sap.
I have searched a bit and had also asked on an HRS listserve about the toxicity of pine twigs and cones.
I came up with this information:
Rabbits may eat the twigs, needles and cones of pine trees, even unbaked, as long as they are free from any pesticides and bug-free. You may decide to bake the cones to be extra safe, ticks and parasites can hide inside the cones.
Be careful with other conifers (evergreens), not all of them are safe.
I include a photo of pine twigs here from wikipedia as I was surprised to see how different they look when the shoots are young:

young twig on left, mature one on right