I did not read all the replies, but will give you my scenario and my dad's scenario.
FYI - I got married at 33, and if you think cutting, splitting, and stacking wood will be eating into your free time, wait until you have some kids. Hunting, fishing, shooting, and cycling went down slightly right after home ownership and marriage, but they have almost disappeared after having kids. Want to talk about money? That has pretty much disappeared too. lol Since the Great Recession, we have been maxing out our retirement accounts and the kids' college funds, so working on cars has been more to keep them running than to modify any for speed or off roading. Using wood to heat the house instead of oil is so we can save $2,000+ a year and also be somewhat independent of the utility companies. Debating putting in an electricity generating windmill too so we can do without the utility companies entirely. Keep in mind, that after what my wife makes and the FICA/Medicare that I have to pay, $2,000 after tax dollars is essentially $4,000 of net income before taxes for me. So, not really a drop in the bucket when it comes to billable time. That is essentially 30 billable hours for me. Plus, last year we had the thermostat at 68 degrees and wore sweaters. This year, we have it at 75 degrees and wear short sleeves. If I really get sick of cutting, splitting, and stacking, I will crank it back down to 68.
I am 41 years old and just started heating with wood this year. In general, everything you do has an opportunity cost. Me, I enjoy being outside and working with my 70 year old dad, so that is some pleasure derived from cutting, splitting, and stacking wood. We just split 2 truckloads of wood yesterday with the help of my brother in-law and it took us about 6 hours from start to finish. Still need to stack the stuff though. I took a truck load and my dad took a truck load. That should be a month's supply for both of us and we are both 3 years ahead, if not more, with our wood piles. I eventually hope to get my daughters and son involved in the process and just this morning taught my wife how to start a fire in the furnace.
My parents used to "heat" the house with a fireplace and natural gas, and the fireplace was very inefficient. Two years ago, right after I bought my wood burning furnace, and to the dismay of my mother, my dad finally bought the insert he had wanted for a decade. Now, my mom wants a second one for the upstairs. The basement is so warm now, that they hardly leave it during the winter. Their utility bill has gone down and their house is a lot warmer. At 70 years of age, my dad can no longer lift the large logs, but that is where a cant hook and my brothers and brother in-law come in. However, my dad can still run the handle for the splitter, he can stack in the truck, he can cart small loads to the truck, etc. I am guessing he will still be at it until he is 80+ years old.
If money is not an issue, then I would surely use the natural gas instead of the wood burning furnace. If I was so busy at work (i.e., I bill out a lot more hourly than what I can obtain in wood) that I could not find time to cut wood, then I would use the natural gas. If I truly hated being outdoors cutting, splitting, and stacking, then I would use the natural gas. Ultimately, it comes down to a lot of things for me because I am pretty tight with money, I like being somewhat independent, and I don't really hate cutting, splitting, and stacking. However, you will not find me cutting, splitting, and/or stacking during tax season (i.e., my busy season). Ultimately, you need to decide how much the monetary savings means to you versus missing time doing other hobbies. For me, cutting, splitting, and stack is just another hobby, like working on cars, hunting, fishing, shooting, cycling, working on the house, etc. I am never out there cutting, splitting, and/or stacking and wishing I was out hunting, shooting, cycling, fishing, etc. Now, ask me about mowing the grass. All I can do while I am on that mower is dream about hunting, fishing, shooting, and cycling and then the landscapers bill bursts the dream. If money was no object, somebody else would surely be mowing my grass. Cannot wait for the kids to get old enough to run the zero turn, edger, trimmer, etc.
Simply put, the variables are different for everybody. My dad has been retired for 8 years and this stuff keeps him busy. Me, I have my own law/CPA practice and I usually have some downtime during the middle of the summer and late November to the New Year. I am also very cheap, except for when I buy long term durable goods or anything for my hobbies. I truly believe in paying for quality and longevity, and living well within my means.