In my case, I don't think breathing room / composting were the problem. The leaves I used were dry, and the trees died not because they decayed (they didn't) or got moist (they didn't)... the trees just froze to death. I also wrapped the whole structure with several layers of burlap, for additional protection from the wind (though that was probably insufficient). I think the issue was just that they got too cold, for too long a time.
No need for sorrow though... in my case it was an experiment, and the trees were specifically targeted for this experiment. (They were three-year olds, and had been buried the prior two winters, and kept indoors in their fledgling pots the year before that).
I have seen buried trees begin decaying the bark though (composting, as you say). If they get too wet (e.g. leaves around the stems) or if they lack air space underground, the bark decays and the top of the tree dies back... in those cases the roots may still survive to grow a new top.
Mike central NY state, zone 5