Here is how I cool mine. I put it in water in this rinse tub and add ice after the jars are in.
It looks funny because the fridge in the kitchen has almost nothing but ice trays in the top freezer.
When we have more milk I use another rinse tub. If you have just up to three jars, you can put them in the sink the same way.
The tubs are in the laundry room.
Hope this helps and enjoy that milk!
Nancy