I've lived in California for over thirty years but it was always in a rural area with no home heating burn restrictions. I now live in the Sacramento area, so on this sort of day I can't have a fire in my fireplace (I haven't used it yet, and really signed in today to look at relevant threads to using a regular open fireplace).
Anyhow, as wood burners we all need to accept the fact that it is irresponsible wood burners who cause this sort of thing. From burning garbage to burning wet or green wood, or throttling down an airtight to the point it's barely still burning; we all know what makes the smoke and we know how to avoid it. I'll make a bold statement: if everybody burned dry, seasoned wood and kept their fire going hot enough to avoid billowing smoke, there would be no restrictions (no need for them). Unfortunately we get lumped in with the bozo's who are burning junk or making their fires super smoky that actually cause the problems.
To me it's no different than choosing not to burn on a cool, breezy but very dry day, especially if we haven't really had any rain yet and I haven't cleaned my gutters recently. Likely to cause problems so I don't burn, just being responsible and a good neighbor.
If wood is your only source of heat you're exempt (in Sacramento). I would be surprised if there's not a program through the utility company to assist with insulation or more efficient furnaces for those who need it. If you can afford to upgrade but choose not to, well, I guess it's your choice then.
Local/regional Air Quality Management Districts (burn restrictions) are a different animal from the California Air Resources Board (CARB) with their "guaranteed spill" fuel cans and their diesel restrictions.
http://www.sparetheair.com/publications/CBYB_FAQ_English_2013.pdf
Q: Are there exemptions?
A: The following exemptions apply to both Stage 1 – No Burn and Stage 2 – All Burning Prohibited categories:
• Homes where wood burning is the sole source of heat
• Financial hardship waiver
approved and renewed each burn season by the Air Pollution Control Officer
• Devices that operate exclusively with natural gas or propane
• Cooking devices
• Ceremonial fires related to a specific religious ceremony
There is also an exemption during Stage 1 – No Burn days for those who have an EPA certified fireplace insert or stove,
or pellet-fueled device, and they do not emit visible smoke.