It will work, if designed properly. There is a lot of information regarding using hot water for heating at garygary's site.
http://builditsolar.com/ I would suggest reading up as much as you possibly can before building.
In your climate you would either require a drainback system or ample antifreeze in the system to prevent freezing. A 50/50 mix of anti-freeze will be expensive but then again so will a lot of the other components.
You could design solar collectors to heat the water on nice, sunny days. Using a radiator for heat to air transfer may require a larger radiator than what you have pictured. (or more of them). A hot water system is a lower grade heat than a fire. so the output of air temp is lower. This is why most hot water systems use radiant floors.
Of course any piping running to the house needs to be VERY well insulated to keep losses down. Do remember that water expands with heat, so a low pressure or open system would be the best in this application. The radiator you show won't take any high amounts of pressure.
It may be better to use a system with a large inground storage tank which stores heated water from your wood burner and any solar that you wish to add then install a heat exchanger in the tank to transfer the heat to your house and shed.
that way you could easily automate a lot of the functions you'd have pump loops form your heat source to storage tanks, then a pump loop to the house which could be controlled directly by a differential thermostat.
As far as pre-heating your domestic hot water with this setup, I'd recommend doing a heat exchanger on that, also, which could easily be built. Just remember you want double walled pipe for such an application. You do not want to have the possibility of contamination of your fresh water.
Just try your best to eliminate any losses which would decrease overall efficiency.
You will also want to watch anything that will lower your chimney heat which can cause creosote buildup, a chimney fire is VERY dangerous! You would need to at minimum want to clean the flue once a year..