The idiomatic expression "to snack on one's own" means to eat a small meal or snack by oneself, without any company. It is often used when someone wants to enjoy their food in solitude and not share it with others.
Sentences with «snack on one's own»
Keep healthy snacks on hand so that your hunger doesn't get the best of you. (verywellfamily.com)
We ended up freezing half the batch and they have been great for snacks on the go. (iheartnaptime.net)
While weekly meal prep will certainly set you up for success, it's also important to ensure that you have healthy snacks on hand at all times. (lifesum.com)