Somehow manufacturers have not completely gotten away from this image and still make night creams that are heavy and greasy. Just know your night cream is more of a treatment cream and should be designed to tackle problems specific to your skin type. This does not have to affect the thickness of the cream, however. Oily skin wrinkles less. Lines and wrinkles are formed from a breakdown in collagen fibers over a long period of expressing, sun exposure, and just plain time.
Oily skin does keep a lipid or oily film over the face, which does keep it moisturized and supple.
The sebaceous or oil glands, however, have nothing to do with collagen fibers. It tends to form one or two deep wrinkles, whereas thin skin usually has many very fine lines. Think of a piece of heavy wool versus a thin piece of silk. When folded, the wool will only crease in one or two places, but the creases will be deep. The silk may form many creases, but they will be superficial.