Looks like your trip is done by now, but for future reference by others:Â I was there 10 days ago and the first kilometer of the South Kaibab was a lovely packed powder and I had absolutely no need for anything on my Merrill Moab low-cut hiking shoes:
Then, as is almost always the case, that seep at a eastern switchback 1 km in had a clear ice layer that got me onto all fours to transverse it and then I relented, sat down on a rock and put on a 10-stud rubber overshoe thing ($9 on Amazon):
Which was exactly right (for me, on that day) – I could walk upright (with a smaller stride where the ice was), they stayed on, and gave plenty on traction in that zone that thaws and refreezes into solid ice. I felt no need for trekking poles (I had them back in the rental car, but had scoped the trail the night before).
Most people were wearing more Yak Trak style devices, but those are heaver and sometimes less secure. A few people had four point instep crampons and I’ve brought and used those at times, but they rarely stay snug on your boot for long. Very few people had full, 10- or 12-point crampons which is always overkill for that very substantial, modestly-sloped trail.
I suppose you could get a big dump followed by several freeze-thaw cycles and have the first 1.5 miles to traverse with some traction aid, but I usually find the upper km is fine and then there’s 500-800 m of transitional icy trail and below that, it’s slushy and muddy until it’s not.
The grocery store at the Market Plaza inside the park is usually well-stocked on traction devices (and fuel canisters) although shortages can arise. I always bring a few styles with me and then always scope the trail the day before as I stretch my legs after the flight down.
Even if you don’t normally bring trekking poles (I don’t) – it wouldn’t be wrong to bring one set between you so if a particular hiker wants that reassurance or their traction devices aren’t working for them, you’ve got an option.
Remember, there’s no water at 1.5- and 3-mile huts in the winter. No water until you get to Indian Garden which is more of an issue on the way back up, or if you go part way in and back out without getting that far.