Heating your home with firewood can be cheaper than heating your home with natural gas if you can get the wood for free or very little cost.
Around here a cord of wood costs $250.00 and you would likely need 5 or 6 of those cords of firewood to heat your home through winter.
At $250.00 per cord times 6 cords it would cost $1,500.00 per year to heat your home with wood.
Natural gas heating for me costs around $168.00 to $200.00 per month depending on how cold it is here so I would usually pay a little over $1,000.00 so I save around $400.00 to $500.00 per year heating my home with natural gas over wood.
Plus with wood you have all that work whereas I can work at my job and earn more per hour than I would saving money working preparing the firewood.
So in my opinion heating with firewood costs more than natural gas.