Even if you were to have $15k into an ATV (or even better a UTV), chainsaw, splitter, wood stove, and other various items used to burn wood it still works out to be a cheaper option for most. Everything listed will have a 20 year minimum life expectancy (I still use an 86 Honda 3 wheeler). A conservative number would be 150 gallons of fuel oil is equal to 1 cord of wood. That works out to about 450~500 gallons of fuel oil for 3 cord. Or about $1500 in fuel oil costs. So in about 10 years you will have paid off that $15k investment and in another year or two you would have paid off consumable costs (like gas, oil, chains, etc). That's assuming you have land with wood on it. It also doesn't take in account that you could use the ATV and chainsaw for non wood heating tasks. if you buy wood then your investment would be much smaller, no chainsaw, no splitter, no ATV.
So now you need to decide what your time is worth. This is not as easy as you would think. I find splitting wood is kind of therapeutic being outdoors and no stress, not sure how to put a value on that. There's your time vs the exercise you get. If you don't have time then it may never be worth it. The same can be said about doing your own maintenance to vehicles you own. Between the cost of the tools and your time it might not be worth it. For others it makes sense.