How do you manage your skin type that changes with the seasons?

My skin is extremely oily in the summer but extremely dry in the winter; my skin type swings between the extremes depending on the season. During this time of year, as the seasons change, sebum comes out while my skin feels tight at the same time, and I really don't know how to manage it. If I stick to light, hydrating products because of the excess oil, my skin feels tight, but if I use anything with even a little bit of oil, my face just gets shiny and greasy... It's my skin, but I don't know what I'm supposed to do. I figured the oiliness is better than the tightness, so I've been focusing on products with good moisturizing power, but the oil rubbing off onto my hands is really annoying. Is there no way to keep the surface matte without feeling tight? How do people with similar skin manage their skincare these days?