Gas is a fossil fuel. When we burn it, it generates carbon dioxide and equivalent emissions. The best way to cut carbon from your winter heating is to get off gas. Any time a gas system or appliance breaks, replace it with an electric one. Reverse cycle heat pumps are a great choice.
But if you're not ready to switch, you can cut carbon by dialling down the heat. For the average Canberran, turning down gas heating by three degrees saves 0.2 tonnes carbon per person per year.
Data and references in the 'Notes' section.