None of the wood I have bought (or bartered for) has needed to be chopped once we get it - it all comes pre-chopped. If I'm paying for wood, I expect it to be chopped to a size suitable for a woodburner - I'd refuse the delivery or haggle down the price if it wasn't. Free wood might need to be chopped, but we (or rather, my husband) thinks that is a small price to pay for free wood (he likes chopping, thank goodness.)
Woodburners aren't banned outright in Christchurch, though. The rules for the use of woodburners in Christchurch can be found
here. My understanding is that Christchurch has been divided into two zones: in zone 1, if you have an existing woodburner, you can continue to use it in winter months if it's less than 15 years old (you have to stop using it as soon as it's 15 years old), or you can replace it with an approved, low-emission woodburner or pellet burner, but you can't install a woodburner if you don't already have one (though you could install a pellet fire subject to resource consent). If you're in zone 2, you can still use your woodburner, regardless of its age, but you have to use dry wood with a moisture content of less than 25% (who'd want to use wood that was any wetter, anyway?) or paper or cardboard. You can still install approved, low-emission woodburners in zone 2, though you'll need to get building consent.
But wherever you are in NZ, or in the world for that matter, ideally you want to be using a modern, low-emission woodburner and well-seasoned (dry) wood (from sustainable resources) to reduce the amount of smoke produced.
And all of our wood - even the free stuff - comes from renewable resources, and is therefore carbon neutral. I've never had a problem sourcing wood from sustainable resources - even the free stuff - but maybe that varies by area? The Coromandel is well known for being full of hippies, so maybe that makes it easier for us to find eco-friendly wood.