Chris,
I have a different view. While oak, maple, and other hardwoods are best for burning once you get a good fire going, quick burning woods such as pine and other softwoods are great for getting a good fire started and the chimney heated up quickly. That quick heating is desirable to prevent creosote buildup in the chimney. Willow should be good for that as well. I have burned some willow on occasion. These 'low heat' woods are great for the 'shoulder seasons' when you just want a little bit of heat.
If you split it and let it sit uncovered the whole summer it will be dry enough to burn come fall. Re the water content---I helped a friend cut a birch down and it too was dripping water or sap.