Since nobody else has answered, I'll try to help. The snow will be icy, but it's not too steep. There may be enough debris and depressions in the snow to allow you to get to Matterhorn without crampons. On the other hand, you might slip and land on your ass (or worse) a bunch of times. I would bring instep crampons or something similar. I think heavy boots, 12-point steel crampons, and an axe are overkill.
I agree with Bob. I imagine that you'd do fine with some light crampons. I did the easy class 2 southeast slope in early August and didn't set foot on the glacier portion but judging by snow/ice elsewhere nearby I think light crampons would be fine.
I visited that area for the first time last weekend. Awesome. I don't think I caught a glimpse of the North Arete, but you can probably get a guess on the not-so-much snow conditions here, North Yosemite denuded:
Warning: a LOT of pix, no captions, I'm working on it. A lot of peaks and passes I want to revisit.
The rangers up there were real cool, the guy at the Bridgeport station and the fellow I met at the trailhead. They helped me work out my itinerary and campsites, on the fly, permits were no hassle. Up to Barney Lake (late start), around the donkey passes, up the SW and down the SE, Horse Creek. Real neat.
Just a look-see, next time I'll see that ridge I hope they'll be wearing white shirts.