I've done probably 10 traverses in the past 3 years. I think 4 of them were "official" winter traverses. I don't know if I'd say that I'm a guru, but...
In full winter conditions, doing it as an overnighter is "easier" because you can camp above treeline on the snow. If there's no snow cover, though (I think the official rule is 2 feet), you're not allowed to camp above treeline...and thus you have to lose a lot of elevation in order to find a decent place to camp.
So, in October, I'd say it's best to do it as a day hike...assuming you're in decent shape. Of course, it' all weather dependent up there. You've gotta be able to wait for a good weather window. If the weather sucks, even the most experienced will be hard-pressed to make it over the ridge in a day.
I'd estimate an October traverse would take about 12-14 hours to complete, for most people. You'd definitely want to bring Microspikes (or something similar), and probably crampons. It'll definitely be icy up there.