Do counter top ice makers keep ice frozen?
Yes, built-in ice maker machines are insulated or have refrigerator ice storage to ensure that all of the ice in your bucket stay cold.
Built-in ice machine makers are fed with a water line and so they are essentially a mini fridge. They are quite a bit more expensive and this is one of the main reasons.
It is also VERY important to note that most of the portable ice maker machines do not keep the ice frozen. You will be spending quite a bit less on them.