Chill mugs?

Maybe a silly first question, but: Do you chill tiki mugs as you would classic cocktail glasses?

You can, but mostly you don't. Tiki mugs take up a ton of space in the freezer and due to their mass, they take forever to chill down. I will fill the mug with ice while I'm making the drink, but that's about it.

I don't chill my tiki mugs, but I have a set of metal tumblers for 151 Swizzles that I keep cold and frosty.

Freezer would be overkill, and may cause more damage to the mug if you are leaving them in for extended periods. Placing them in the fridge for a while or filling with ice and water while mixing the drink should do the job. You want the glass cold but not so cold that the drink starts to slush in the container.

I do, but as mentioned, just use a mug(s) that your not worried about damaging. I have two that I use regularly, I just keep them in the freezer. To me, it helps slow down the melting of the ice, so the drink stays as mixed longer before getting watered down.

Is the threat of damage really all that serious? I've been freezing the same 2 martini glasses for years and I haven't noticed anything off about them.

It makes them more brittle and increases the odds they will shatter one day.