Worry about water.
While your diesel will not substantially degrade over the winter it could pick up some water. Flling the tank doesn't prevent this as you can't have fule against all surfaces without having overflow when the temperature climbs or pace when it drops. Fuel conditioners combine with the water so you get rid of it as you burn the fuel. Power Service does well and can be bought at any truck stop. We may have wasted a few bucks on conditioner but we operated and stored a Yanmar diesel over a 22 year period, and left it for 2 years once without any difficulty.
