What the alternative for heating? If it is AC, consider that much of the electrical grid is powered by air pollution anyway (especially coal), so the issue is at best deferred.
In urban areas, I believe the biggest cause of air pollution is vehicles, not woodsmoke.
If anything they're the opposite. The petitions themselves are not binding, and if they're not directly to institutions then they're probably not even noticed.
...but they do convince signers that they've 'done something', the catharsis of which makes them less likely to do something that actually matters.