Can you freeze oatmeal?
Yes, you can freeze oatmeal
Best quality within 8 months, depending on the kind.

Where these times come from. USDA FoodKeeper has no entry named "oatmeal". The 2 kinds on this page are the USDA entries that cover oatmeal, copied without change from Cereal and Oats. Each row in the table is one USDA entry; pick the one that matches what you have.
cook-before-eating cereal (oatmeal, etc.)
No freezer guideline
whole grain oats
Up to 8 months
What the freezer time means
Freezer times from USDA FoodKeeper are about quality, not safety. Food kept frozen at 0 F (-18 C) stays safe indefinitely; what changes over the months is texture, moisture and flavour. Wrap oatmeal tightly, press out air, and label the pack with the date so the window above is easy to track.
Thaw in the fridge, not on the counter. Anything that thawed in the fridge can be refrozen, with some further loss of quality; anything left at room temperature for more than 2 hours should not go back in.
Storage habits that make the difference
Store dry pantry staples in a cool, dry cupboard away from the stove and direct sunlight, ideally in airtight containers once opened. Reseal cracker and cereal bags tightly with a clip or transfer them to a container to keep them crisp. Label opened jars with the date so older ones get used first.
Can you freeze other shelf stable foods?
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.