Whether you store the oatmeal cups on the counter, in the fridge, or in the freezer, the most important thing to follow is to let them cool down completely before sealing them into a bag or container. If you put them away while they are even slightly warm, the condensation will ruin them. You can store at room temperature for 2-3 days, in the fridge for 4-5 days, and in the freezer for up to 3 months.