Pine (and most other conifers) pitch is flammable and will burn even if it's relatively green. Hardwoods, not so much.
Careful, there. This could be misconstrued as some really bad advice. In fact, this is the basis of why so many errantly believe you should not burn pine.
Yes, Pine will burn when wet, more a problem than a feature, as burning wet wood is the best way to end your season (or home ownership) in a chimney fire. It is fine to burn pine, but it must be dry to do it safely.
When burning wet wood of any species, you're putting an enormous amount of thermal energy into converting water to vapor. This vapor, the droplets of which condense onto creosote-producting particulates (just like rain drops!) travels up your chimney, where it will condense and deposit creosote in the chimney. The wetter the wood, the more energy lost to conversion, the cooler the exhaust, and thus the higher fraction of particulate-carrying water droplets end up condensing on the pipe before reaching the top and exhausting. It's an exponential problem.
So, yes... wet pine will burn. It also carries a higher fraction of resins that lead to creosote production, making the fact that it will burn while still wet even more dangerous. But be safe, don't do it. Burn DRY wood, no matter what the species. This will minimize the energy lost to conversion, minimize the water you're putting into the exhaust, and keep your exhaust temperatures higher such that the small amount of water it still contains will safely make it to the top of the pipe before condensing.
As an aside, if you ever wondered why flue probe thermometers have a "too cool" range, this is it.