I live on 25 ha of forest, have an axe and saw, and heat with wood. Let me tell you: you want to use the saw for everything but splitting. Axes are fine for burly cavemen.
Anyway, in a cold climates like mine an acre would not be enough to keep you warm because trees grow slow when it's winter six months out of twelve. It takes a lot of wood to keep you warm, and one tree gives surprisingly little wood. After a handful of years you'll have clearcut your measly acre and still have another couple of decades to go before it becomes harvestable again. I'd say you want at least 10 acres if you manage it well and the soil and drainage are at least half decent.
They grow faster since they already have a root structure, the size is consistent and the wood is generally straigter (the japanese have a similar technique for extremely straight cedar logs)
By the time you get to 100 acres you can basically heat your house with the stuff that blows over in storms and the remainder can yield a nice cash crop every couple of years, giving space for the other trees to grow. Personally I'd prefer a chainsaw for anything but the most incidental cutting, and a hydraulic woodsplitter (rented) to get the job of preparing firewood for a while year done in a short time.
Anyway, in a cold climates like mine an acre would not be enough to keep you warm because trees grow slow when it's winter six months out of twelve. It takes a lot of wood to keep you warm, and one tree gives surprisingly little wood. After a handful of years you'll have clearcut your measly acre and still have another couple of decades to go before it becomes harvestable again. I'd say you want at least 10 acres if you manage it well and the soil and drainage are at least half decent.