How do I prevent cold air from coming through my gas fireplace?

Here's one solution that might help you - https://www.christywalkercreations.com/common_complaints_and_questions.htm

Hi Linda, they sell magnetic Fireplace vent covers to prevent the cold air from entering the house. I've also seen people use draft stoppers (like what people use for doors) on their fireplace vents.

Linda: you may want to check to see if the flue is closed when the fireplace is not in use.

Hello Linda,

Is your flue closed and still having a draft?

We had a similar problem installed a top closing damper to our leaky —wood burning fireplace chimney.

Here are possible options, hope they might help address your situation.

I tried making a wooden cover/ screen but that was ineffective.

We look at the chimney balloons as an option on Amazon but with them costing $50 and needeing to be removed and replaced with fireplace use -we decided to purchase a pull down option that works marvelously.

https://www.rockfordchimneysupply.com/chimney-dampers/top-sealing-chimney-damper-caps

The balloons are available in many sizes, you would need measurements to determine your size and cost.

Fireplace dampers are inefficient due to warping and misalignment from frequent heating and cooling. A bad damper can cost you up to 30% more on your heating bill. Your fireplace damper is releasing your indoor heat and letting in cold outside air! The Chimney Balloon is a inflatable blocker that prevents drafts from a chimney caused by a broken, warped, or missing flue damper. It even works in chimneys that have no damper! The Chimney Balloon stops this heat loss by acting as a chimney blocker to insulate your fireplace and save you money, heat, and comfort.

https://www.rockfordchimneysupply.com/chimney-balloon.php

https://www.amazon.com/Chimney-Balloon-Inflatable-Blocker-Medium/dp/B000MIO394