Wet wood chips better, as the moisture lubricates the knives and helps them stay cooler. This is the same reason green wood chips better than dry wood. The manual for my Wallenstein says to avoid chipping dry wood if possible. I have actually seen dry wood cause smoking in the chipper!
If really too wet, can gum up in the chipper though. I often kept a small pile of dry stuff to throw in every so often if chipping/shredding wet or greenish material.
When I collected leaves in the fall of our very wet 2018, they were far too wet to run through the shredder. I just had to pile them up on my compost pile and let them degrade. Took a lot longer.
Think limbs and stuff would have to be pretty wet to not chip well unless they're wet and green.
I'm also in your neighborhood, in Snohomish, Washington, and I have a Woodmaxx standalone chipper. The instructions for the machine actually tell you that green and wet wood is better for the chipper, because the moisture acts as a lubricant. The chipper loves eating entire vine maples, by the way. Do take care in feeding lots of moss-covered stuff in, however, as it can jam the machine.