I have one of these, it holds ice in the bottom and the little plastic cups slip right in.
I used to use it for lots of stuff now i just put my limes in it. In hot weather the ice melts fast so i built myself an insulated box that holds 6th pans.
Notice the aluminum box on the top of my cart; it has a red cutting board resting on it. That is my new cold box, the outer area is made of stainless steel, the inner is thin aluminum sheets. In between is some r4 rated pink hard foam insulation 3/4" thick. The top piece is a daimond plate aluminum piece that is removable so i can access the inside for cleaning/ repairs.