Heating your home with wood can save you money if you're able to get most of your firewood for free.
If you have to buy wood at $250.00 to $300.00 a cord each month then you'd likely be better off heating with natural gas if it's available.
Heating with wood even when buying firewood is certainly much cheaper than heating with heating oil or even sometimes propane.
Heating with heating oil can cost as high as $4,000.00 to $6,000.00 per year but wood heat would cost you probably $1,500.00 per year depending on size of home and cost of firewood.
If you have natural gas available and have to buy wood then use natural gas as it's likely cheaper to heat with natural gas than wood.
But if you have propane or oil only available for heating then wood would be cheaper but requires some work.