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.