@Krone
A lot of my trees are hanging on to their dead foliage this year (crapes, maples: Japanese and amurs, hornbeams: Korean and carolinia, elms: Chinese and alata, etc...)
This is mostly from our temps going from night time lows in the 50s to mid 20s for a few consecutive days. The foliage got freeze dried and didn't go through its normal change this fall.
I suspect a lot of trees hold on to their foliage during winter to insulate the newer axillary buds, especially in cases where there wasn't enough time for normal/complete leaf drop; these buds may need extra protection from the cold.
I wouldn't cut them off at the petiole unless it's really bugging you, or like Paradox said, to keep your overwintering area cleaner and bug and fungus free.