If you're "scrounging", please do ask the owner's permission. We own a large tract of land, and more than once we've caught people out cutting up a fallen tree without permission. This is not only a matter of theft, but IF those people were to be injured on our property, they could potentially sue us. Yes, you may find too-busy homeowners or little old ladies who'll be glad for you to come in and cut up their fallen trees, but never, never assume.
Also, recognize that heating with wood exclusively is a big undertaking: Unless you own property yourself, you're not likely to find enough free wood to heat all winter; and cutting firewood is hard work. For most people, it's more realistic to supplement with wood.