No, you can’t. Yes, you are missing the first law of thermodynamics. The refrigerator doesn’t ‘make cold’, it moves the heat from the front to the back. Pull your refrigerator out and you will notice the back is very warm.

If you put the back of the refrigerator out your window, it would cool the inside of your room, but it wouldn’t work as well as an air conditioner because it is designed to keep a very small highly insulated area cool. Air conditioners use the exact same principle, but they are much more powerful because they need to move a lot more heat.