I actually did this "hike" without snowshoes. Probably the only year I could get away with it given how little snowfall there was. The temperature was astoundingly warm for the time of year, and the ski resort below was scraping by with patches of dirt poking through the melt.
This is a great climb though with fantastic views. It really gives an amazing panorama of the area, including the highlight, Shuksan. I did this in my waterproof hiking boots and did just fine, but that may have been a fluke with the weather. I'd imagine this gets pretty powdery in the dead of winter on a normal year. Once I reached the top I was treated to some pretty blustery winds and cooler temps, but it was still bearable with a few layers and waterproof clothing. I brought my film camera with me and it was a real challenge changing film at the top with the howling wind. My fingers just about froze in the process.
It's neat to see all the snowshoers, skiers, and snow campers at the top. Tents were lined up, and tracks covered the entire summit area. I really enjoyed the hike up and the views, and would recommend this to anyone wanting to get a great look at the North Cascades for how little effort is needed to get to the top. Or you could just do it in the summer when the road is open and you hardly have to hike at all. Up to you!