It’s possible (and indeed likely, from the studies linked in this thread and article) that cold weather contributes both to gas usage and asthma, and gas usage contributes to asthma on its own.
As an aside -- it's important to keep in mind that the article does not say "gas stoves cause asthma, rip them from your homes immediately or be prepared to curse your infant with respiratory illness." It says, "there's a link here, and we should do something about that link." The author goes to great pains to use words other than cause: "connection" "link" etc.
From the article:
> The cumulative evidence was enough for the venerable New England Journal of Medicine to publish an editorial in January recommending that “new gas appliances be removed from the market.” It was co-authored by Howard Frumkin, a former director of the CDC’s National Center for Environmental Health, which is responsible for investigating environmental drivers of illness and promulgating guidance about those risk factors.