Woodstock recommends a light scrub with #0000 steel wool to clean the glass. I’ve been doing that once or twice a season fo 15 years or so. Seems like they don’t think moisture is good around the gaskets, so I never wet mine, and it still cleans up nice. Finish up with dry paper towel.
damp paper towels or newspaper all i have ever used, as i do not get any papers delivered, hence paper towels.
Never had anything I could not clean off the glass with just a water wet paper towel dipped in Ashes , then wipe with clean water wet paper towel, then quickly buff with dry paper towel