When freezing milk, use an airtight container and be sure to leave at least 1/2 inch headspace at the top (or 1½ inches if you’re using a narrow-mouthed container) as the milk will expand when frozen. Thaw the milk in your refrigerator and plan to use it within two or three days.hen it comes to drinking the milk, it’s a good idea to do a trial run first — freeze a small amount, thaw it and see how you like the outcome. From a quality standpoint, skim and low-fat milk usually fare better throughout the freezing process than whole milk.