How do I keep cold air from leaking into room from exhaust fan?

I have a light/exhaust fan in my laundry room. It is vented through the garage attic and a ton of cold air leaks into the room. I have insulated around the housing in the attic but it is still very cold and it affects the efficiency of our home. Do I really need an exhaust fan in a laundry room when the electric dryer vents to the outside? Can I use a regular ceiling fixture in place of the exhaust fan , and if so how do I fix the huge hold in the ceiling?

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