Move over commercial wood stove glass cleaner. There's a better option in town, and it'll cost you 2 pieces of paper towel and some H2O:
Observe the morning after a nice, comforting fire. Your glass is bound to be dirty. There's a quick and easy solution. Grab two pieces of paper towel, and a spray bottle filled with tap water.
I'm cheap so I use those choose-a-size towels. Two little pieces will do for me. Give the (cold) door a quick spritz, and the folded paper towel too.
Then dip your moistened paper towel in some white ash, and go to town on the door.
That's IT. I mean it. Spray your door with your water bottle once more, and remove the residue with your clean paper towel. I've been doing this for years, and I promise you it's so much easier than those drippy, messy commercial cleaners.
Voilà! Sparkling perfection. Everything in life should be this inexpensive and easy. Total time, start to finish? A grand total of 3 minutes, photos included.