It’s a small, stainless-steel sink set into the counter, and it has only cold running water. Does one wash glasses in it, despite it having only cold water? Is there any particular reason why there is one of those (I assume pressure-enhancing) crook-shaped faucets on it?
You can do a lot of things with it but is basically a place to dump old drink contents out, rinse the glass, and make another one. Other things in a lively bar tend to need rinsing too such as a knife to cut fruit etc.
Yep, not used for anything other than mixing drinks or rinsing utensils. Not very useful unless you use a bar often.
God, I’m really living high, I’ve got hot water! 
Hey, I’ve got hot water in mine too. We must be living high on the hog here. 
It’s more useful as a drain than as a sink, though - toss the remnants in there, throw out ice, etc. And you can rinse your glasses or use it to help you wipe up a sticky spill or rinse your hands off.
It also serves as an emergency urinal.
As we’ve got hot water, too, ours came in incredibly handy while we were remodeling the kitchen. No, you can’t wash dishes in a wet bar sink very easily, but it’s sure a hell of a lot easier than washing them in the shower!
The water I get out of it primarily goes into a coffee pot, the sink is a drain for dumping used ice into.
-lv