A cold coffee is sometimes called Mazagran coffee or even simply Ice Coffee if it contains Ice.
The Mazagran coffee is a cold coffee that is a sweetened coffee that originated around the year 1840 in Algeria.
The Mazagran has been known to be the original iced coffee.
There's also a frozen or slushy version of iced coffee as well which is sometimes known as café frappé (à la glace)"
In the USA we usually just call the cold coffee Ice Coffee.
You can also just make some hot coffee at home and add some milk to it and then add some crushed ice or ice cubes to it which is then homemade ice coffee.
I do that myself sometimes and it's a great drink on a hot day when I still need my coffee.