We heat with oil and the math gets more challenging as prices fall/
My conservative assumption is that a full cord displaces about 100 gals of heating oil. Currently this means that a cord I produce on my lot is worth about $220. My records show it takes me 15-20 hours of hard labor per cord from standing tree to stacked in shed.
My hourly rate has fallen from $20 to around $13.
On the plus side it's tax free and after 2-3 hours in the woods I've got my daily exercise and then some.
So I'll still be out there for at least 3 more seasons and taper off at 70 after 40 years
From BTU ratings charts ( they don't all agree on precise exact numbers )
one cord of red oak = 24,000,000 BTU
one cord of eastern white pine = 14,300,000 BTU
one gallon of HHO = 138,700 BTU
24,000,000 / 138,700 = 173 gallons of oil equivalent
14,300,000 / 138,700 = 103 gallons of oil
Today, a gallon of HHO is $1.68 here, so a cord of red oak would be "equivalently worth" $290.00
So if you bought that cord of oak for $250, in simplistic terms heating with wood would seem cheaper.
But it's not.
Depends on how many BTU your appliance turns into heat and how much of those BTUs go up the chimney.
If your wood stove is 70% efficient then that $250 cord of red oak nets 16.8 million BTU of heat. $250 / 16.8 = $14.88/ one million BTU
If your oil burner is 70% efficient then one million BTU costs you $17.30
-(oak) wood is cheaper to heat with
If your oil burner is new and 90% efficient then one million BTU costs you $13.50
-HHO is cheaper to heat with
Oak - $14.88
HHO(70%) -$17.30
HHO(90%)-$13.50
For some people, HHO is most certainly a cheaper alternative for heat right now. For some it is a wash, others - not too much more.
I posit that the average person isn't likely to buy and heat with wood unless there is a significant savings to be gained for the extra work involved.