Small-leaved Linden Trees from Seed

This Autumn I am planning to try something new: I'm going to collect a bunch of seeds from local Small-leaved Linden trees (Tilia Cordata), put them in the fridge for a few months to cold-stratify them, and then plant them this upcoming Spring. The first big question comes up: do the seeds have to be peeled out of their little nutlets first? Or are the seeds thrown in the fridge as-is, nutlet and all?

I have read that for linden, remove them from their woody fruits, and soak them in hot water, then stratify them for 3 to 5 months in a cold, moist environment.