Yes, goats can eat pine cones.
A user on a forum had shared his experience saying:

That his goats love pine cones and have never gone sick because of eating them.
Pine cones contain Vitamins A, C, and D. Fiber which helps the digestive system. Magnesium and Calcium for strong bones and teeth.
Iron increases hemoglobin production. Manganese is a very important trace mineral to goats especially during pregnancy as it aids in healthy hoof growth.
Phosphorus strengthens goat kids’ bones, teeth, and muscles. Potassium that aids in the development of strong organs and resistance to stress.
Zinc helps with growth, reproduction, and tissue use of other nutrients.
Are pine cones bad for goats?
Some pine cones can be bad for goats if they eat a large amount of them. Pine cones contain azoturia which is a type of poisoning caused by eating pine needles or cones from certain conifers such as pines and yews.
It causes the muscles to break down resulting in severe pain, gait abnormalities, weakness, and even death.
If you suspect your goat has eaten a large number of pine cones, call the vet immediately!
Pine cone poisoning is mainly caused by ingestion of male bracts and female seed cones. Symptoms occur within five to ten hours and include:
- Abdominal pain and muscle trembling
- Profuse sweating and urination
- Increased heart rate and respiration
- Elevated temperature
What should I feed my goats instead?
You can also feed your goats grass hay.
It will help maintain strong teeth and bones, along with it being the best source of fiber.
Don’t let them eat too much though, they meat bloat or get an upset stomach.