As long as your wife's fear of the fire can be turned into a healthy
respect for it, she'll do fine sharing the responsibility.
Over here it's me and two cats, but my girlfriend spends a lot of time here.
GF initially sat back and let me manage everything -- lifting, cutting, splitting, stacking, and burning. One day recently, instead of sitting around while I was processing a load of firewood, she put on work clothes and started helping me with it. I taught her how to use the chainsaw, the splitter, and the maul/wedge. There are few things more satisfying than hearing your woman say, "We need to buy a more powerful chainsaw".
With regard to burning, I discovered that welding gloves (3 pairs for $9 at Harbor Freight) helped alleviate her fear of reloading the stove. The gloves go nearly up to the elbow. You can get a lot of work done with a blazing hot stove without coming close to burning your hands.
We've started a small contest around all of it. Whose cuts/splits are more uniform, whose load burns better, etc. She's competitive, so this helps to keep her interested. She always wins. This means that we both win.
Heating with wood has so many things that resonate with both genders. We get to play with power tools, we can be barefoot in the living room when it's brutally cold outside, we spend a lot of time together, and we cut the gas bill in half.
It is a lot more fun because we work on it together. She now understands (and participates in) my obsession... except for staring at the woodpiles, but I think that's specifically reserved for guys with cold beers. Also, I doubt that I'll ever get her to help me clean the chimney, but that's understandable
Give it some time, and she'll take an interest.