I would suspect that if you were to light a fire right now you'd get a LOT of smoke in the house until the heat melted through the snow cap.

What you might try doing is putting an electric heater in the firebox and closing the door.

The heat will eventually get up to the snow pack and start melting it, but it's probably going to take awhile.

kframe19 -- thanks for the response. I actually resorted to a low-tech solution of the same basic type today: propped a hair dryer on a stool in the fireplace, pointing upwards, and just let it go. Probably not ideal for the hairdryer, but it's an old one and I don't have a space heater. Seems to be working! (I also tied one of my dog's soft rubber balls to a rope and pitched it up at the chimney cap a few times, which knocked some of the snow off and poked a few holes where I can actually see the mesh of the cap. I'm going to give a fire a try -- making sure it draws properly first (which we always have to do since this is on an exterior wall). I'm hoping if at least half of the cap is free of snow and visible, that I'll get enough air flow to work, and the rest should melt quickly after that...which would be nice, since we have another foot of snow and ice coming tomorrow!

I envy you your ability to have a fire. I don't have a fireplace, and I have a heat pump system. Not exactly warm heat.

I've been threatening for years, but I think I should be able to swing it this year -- I'm getting a pellet stove.

if you have a couple of cans of sterno, or some denatured alcohol, you could put those in the fire place and light them off.

They won't create any smoke, and two or three cans of sterno or a pie pan of alcohol will create a lot of heat to melt through the snow.

Hopefully, though, by this time you're toasting your tootsies by a roaring fire...