I use my snowboard boots, a lot will depend on the snowshoes you use. Had to look around for ones that will work with my boarding boots. I carried my boots a couple of times a couple years ago, but the additional weight, and cold boots once your up top sucks. Not to mention trying to switch out in adverse conditions at the top of a hike before heading down.
That said, if your going with anyone other than other snowshoeing boarders you will quickly learn you want a split board or ascent skiis. Sucks breaking your own trail off the skin track