This is an interesting idea. I've wondered about a wood-fired water heater that could send hot water through a tube, too. I don't think the water could be compelled to move through the tube without a pump, though. It could be a mechanically simple pump, driven by heat, but it would need moving parts and fabrication by a skilled machinist. The thermoelectric generator (Peltier thermocouple) idea works. It has been used in quite a number of coffee-can sized woodstoves, for running a fan or charging a battery. A larger (and heavier) array of thermocouples would allow you to use a small off-the shelf water pump rather than a custom one.
I had three other thoughts about your assumptions: First, woodsmoke is much worse for you than the exhaust from an alcohol stove. I recently spoke at a convention where another speaker described his research into the composition of woodsmoke and the effects on people in third world countries who routinely cook over woodfires. He found that woodsmoke contains hundreds of carcinogenic compounds, including PAHs (polycyclic aromatic hydrocarbons) and dioxins. In his study of the effects, his group found that children from families that cooked over open woodfires had substantially lower IQs, poorer fine motor skills, and lower body mass than socioeconomically comparable counterparts that lived in homes experimentally equipped with cleaner burning chimney stoves. He corrected for every imaginable confounder in his analysis. The children in the two groups were in the same areas, in families of the same sizes, were the same ages, had the same health histories, etc.
The volume of exhaust from an alcohol stove is an order of magnitude smaller than a woodstove, it is much lower in particulate (essentially zero with HEET), and the duration of exposure is much shorter (because of expedient lighting and snuffing).
My second thought is that a small woodstove that pumps hot water through tubes will still need to be tended and fed. So having the pump and the tubes doesn't mean that you can leave it alone through a cold night and doze off. As long as you have to get up to add fuel anyway, you could be transferring hot water into a hot water bottle from a pot or kettle. What is the advantage of the pump and tubing over a hot water bottle?
Also, I think in general it is a good idea to be cautious about using gadgets to replace insulation. I think electrically heated jackets, chemical hand warmers, and a planned reliance on fire are unwise. It seems more prudent to me to just bring more insulation than you expect to need, and use fire to keep warm only in an emergency. This approach is lighter, simpler, cheaper, and more environmentally friendly.
As I said, it is an interesting idea. I don't mean to sound critical of it. It could be a fun engineering challenge for its own sake, at least.