A person of refined taste, nothing wrong with that
Stone drinking goblets are very cool. Actually more than cool, they are classy. You can get lots of different ones if you do some searching. You can even get some really pretty fluorite with different colors.
Yes I think they would serve well to keep drinks cold.
I bought some clear crystal glasses for my wife recently. I suppose crystal would count as a stone of course. Hers are clear quartz crystal that has been dyed different colors.