Hi Adelmanto,
In theory : if the cuttings (or plants) start sending energy to make roots, they'll need photosynthesis to keep the flow or reserve of energy - so that means leaves and water and nutrients and heat and light ( ok now the list is sort of not bad :) ).
If you start rooting them now, you're more than likely to get bud break at the same time that you'll get roots and thus you can't put the cuttings to sleep - or you'll loose the leaves.
So I would store them in the fridge and wait until March.
As an experiment, if you have enough cuttings, I would take 3 and put them in a pot with compost and overwinter the pot (in a shed, in a barn ...) as if there was a tree growing inside the pots.
And see next Spring if something comes out .
I did that this year, but then messed up with not watering enough or whatever and so the cutting leafed out and dried out. But this last Spring was really dry here so perhaps just the bad year
for that experimentation and my cutting was really short - it is more likely that with a longer cutting, managing the watering would be easier.
Good luck !