No not in my opinion. If someone says an ice cold drink it usually means it is in liquid form and has ice cubes inside of it or it’s at a really cold temperature, but not frozen. Frozen drink is closer to chopped up ice

No. A frozen drink would be something like a slushy, made with a blender, such as pina coladas, strawberry daiquiris, frozen lemonade, etc. An ice-cold drink could be anything, such as an "ice-cold" beer. It probably doesn't have ice in it, but it is as cold as ice.

Not always. A frozen drink is ice-cold, but an ice-cold drink does not have to be frozen. It can be refrigerated instead.