Pronoun Trouble

Exactly! Particularly when it gets into the slightly more obscure flags - anything outside of maybe the top three or four - it definitely feels more like someone who "gets it" was involved!
I don't know what kinds of things they'd consider putting the design on, as I'm sure they don't want to have it be costly for them, but even just printing the be-flagged logo (in various pride incarnations) on a moderately decent cardstock, even just business-card sized with the hotel info on it, would likely be the sort of thing people would hang onto as a souvenir (which might prompt them to remember it for future stays or to recommend to others.) I know I hang onto that stuff the way I hang on to free pens - they make good bookmarks!
(Also, in my experience when I've gone to Denver's pride fest, the places that DO have obscure flags run out of that merch because people are SO EXCITED to find the thing with their identity!)
It could do a lot of good to cement the hotel as a solidly queer-friendly place to the people who visit, which could spread beyond just the clientele for particular events.

But also a super good point - having holiday-specific logo designs would also be very cute! And again, if it's something that can be printed physically on something a guest could take home with them, it's a sweet souvenir of a holiday or other event they had there... and is also getting the hotel name out there!