Do people with oily skin really need to apply moisturizer?

It might be a silly question, but... haha

Do people with oily skin need to use moisturizer too?

I especially don't want to apply it in the summer.

I'm sure everyone with oily skin can relate, but

My skin feels so stuffy. On top of that, I don't want to add moisturizer.

Since it's so oily, I don't really feel like it's dry.

So in the summer, I just apply a very light lotion and that's it!

Of course, it is a bit dry at first after applying the lotion, but...

Should people with oily skin also use moisturizer?

If that is the case, please recommend a moisturizer suitable for oily skin!