We do. Back when we lived out in the country, we had enough acreage that just the easily accessible dead fall would be more than enough for a winter. Now, in the city, we have a 1.5 acre heavily wooded lot, and the dead fall gives us a pretty good bit. Plus, a couple years back, we had to have 4 good size oaks taken down (drought really hurt us), and our neighbor had around 8, so that has given us a pretty reasonable amount, seeing as our winters are milder.
I generally do all the cutting and splitting in the winter, and not use that wood until at least the next winter. Past few years, we've had enough stacked that what I split each winter won't get used for another 3 winters. Just too hot to do anything in the summer, and I really don't like finding a copperhead or rattler in the woodpile when I'm stacking.
For about 4 years, when I was younger (and this wasn't all that long ago), we heated exclusively with a wood burning stove.