If it is not too late just open the lower draft door, open the vent on top, and build a newspaper (or other type of) fire in the lower chamber. With enough fire and heat it will defrost the gasket enough to open it. I have had to do that several times.
I say might as well cover it. It is true that the egg is made to be outside and the table is made of durable materials, but there are some issues I see. Covering it not only stops rain and snow from accumulating, but also stops UV/sun degradation, rust, and keeps general dirt and environmental contaminants off your equipment. I figure that for the fractional additional cost of a cover, if it prevents or delays failure of metal components (hinge, bands, springs) and wear/fading/damage to table and accessories, it is worth it. I am sure there are other viewpoints, but I always protect anything I invest money in to make sure that it lasts as long as possible. Even if something can be left outside, if I can avoid leaving it outside I do (yard power equipment, furniture, etc).
Mine has been covered and I still notice that some of the color has faded from my table top (heartwood spanish cedar).