Mike D.,
Not to be discouraging, I think it would be a tough slog in there without crampons. In particular, Spur Trail above Randolf Path could be utterly dangerous with out them.
At a minimum, you could get instep crampons for cheap but honestly, I think the money is better spent on some light 8 or 10 strap on trekking style crampons. If you do go the instep route, be sure to get the real beefy ones with proper spikes on them.
Another alternative to consider would be to park at Lowes Store and take Lowes Path up to Grey Knob, and then over to Crag. The lower portions of Lowes will be a muddy "foot bath in the wilderness" but typically Lowes gets more traffic and is more thoroughly boot-packed (hammered?). There will almost certainly be sections of dangerous ice up around Log Cabin. Lastly, be very watchful of the trail intersection with Randolf Path above Log Cabin. Many people (myself included) have mistakenly veered right onto Randolf Path towards Perch. Once you hit Log Cabin, watch carefully to stay on Lowes.
Hope this helps,
Dave