Unlike May conditions,The Ledges in Decemeber are usually covered in ice,most people avoid them, using snowshoes to go further up the gully. Also,don't dismiss the chute so fast. Doing the chute in May can be completely different from doing it in December. Depending on what type of snow year we are having, there could be a thin layer of ice in the chute or waist deep powder and high avalanche conditions.There could even be a cornice that you would have to negotiate at the top of the chute before you even get past the notch. Once past the notch,on the north side, you could encounter a solid sheet of ice. People slide down the north side to their deaths in the summer, I'm sure you can imagine what it might be like in December.
Either way, you should be very comfortable with ice axe self arrest, post-holing, and crampon useage on steep, exposed angles.You have to factor in the weather too. It can change in a flash in late December. Some of the "Bob's" on this website should be able to give you some first had knowledge though. Just my two cents.