I have a couple questions about this subject.

Assuming that the character wants to live a simple peaceful life...

1. Can you sell firewood to at least one person in each hold capital, or are some left with no one to sell to? I mean an official firewood person such as Hod or Hulda, I know any general store can buy firewood for dirt cheap.

2. Can you make even a small profit from relying on smithing alone? If so, how? If not, what would it take?

You should check out "Olaf's Diary" / "Skyrim Rags to Riches" on Youtube for inspiration.

these are so lame ... be a hunter

There should be someone to sell wood to. Every mill location will buy wood. And yes you can make money smithing but only if you find the materials yourself. You'll make very little if you have to buy the materials.

A nice way to make money is mine the ore which also gives you gems like ruby and such. Craft those into jewelry and sell that. Easy money there. Other then finding the resources.

Hunting is a good way as well to make money. Sell the pelts and meat.

Also adventuring out into the wilds, collect loot from caves and such and sell that.

Alchemy. pick flowers and other ingredients and craft potions. Sell the potions. money.

Many ways to make an honest living.

I find these videos entertaining more than I do inspiring. Regardless, I'm going to finish watching them. You actually answered one of my questions because I was looking for someone in or near solitude to sell firewood to, and the video lead me to this guy Hjorunn, which I'll need to find later.

If you're an argonian,an easy way is to catch fish.I made 200+ gold in about 20 minutes