In what way is wood free? To heat even a tiny home purpose-built for high efficiency you'd need several acres of woods to sustainably harvest. For a falling-apart $30k hovel in upstate NY you'd probably need more like 15 acres, and you don't get a 15-acre stand of woods in the deal for that price.
At these electricity prices bothering with wood might not be worth it. If you get some, that’s nice, but otherwise just insulate the house well and you’re golden.