6,700 gallons of water is about 56, 000 (55,811) pounds.
It takes 1 BTU to raise each pound of water 1 degree F.
Therefore it will take about 56,000 BTUs for each degree F of temperature increase.
A cord of firewood contains somewhere between
12 and 25 million BTUs depending on species. Let's assume you're burning white oak at roughly 25 million BTUs/cord to make the arithmetic easy.
Let's assume 50% efficiency for your heater. IThat's just a guess, but I bet it's no higher than that.
I'm also going to asume you need to raise the temperature of your water by 15 degrees F. Again, no basis; another SWAG.
So, the Total BTU requirement to raise the pool temperature by 15 degrees F= 56,000 BTU per degree * 15 degrees = 840,000 BTU
BTU realized per cord of wood = 25,000,000 BTU per cord * 0.5 (efficiency factor) = 12,500,000 BTU
That means that each cord of wood would raise the temperature of your pool by 15 degrees F about 15 separate times. 12,500,000 BTU / 840,000 BTU per pool heating session = 14.88 pool heating sessions
If the assumptions and my arithmetic are correct, even allowing for some additional inefficiencies not accounted for here, a cord of wood would probably easily get you through a 4-6 week shoulder season of weekend pool heating.