Personally I don't bother with cooker etc for day trips, still have a lighter in the safety kit though. I don't take a saw either.
On the flipside I always take food and water in case I end up out there for longer than expected.
If you're somewhere high, steep and cold enough that you might need the crampons then I'd also have a beanie or polypro balaclava, and probably sunglasses for the snow.
EDIT: Ahh now I read the part about the crampons being for wet logs etc, skip that last part.
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