I agree with the "yesses"—this would work. There are alternatives that may or may not be better.
The water heater would be the largest consumer of electricity by far, and would pretty much determine the size of generator needed. Do be aware that all but the smallest of the small water heaters are 220V, and not all generators (particularly smaller ones) are wired for 220V output—very, very few RV generators are. Virtually all electric water heaters are too big to power from a normal 15A outlet if there's anything else also on the circuit (the smallest are generally around 1500 watts).
I would think a propane water heater may be more practical, possibly an on-demand unit.
A very low-tech approach would be to use iceboxes or coolers for the refrigeration and rig up a water heater in the wood burner. If using a hand or foot pump, no electrical system at all would be strictly required. The health inspection people may look askance at such a setup, though—I don't have any experience in that regard.
As to what sort of appliances to get, I would suggest looking for a small commercial sandwich cooler (or, even better, a pizza prep) type of fridge, something like
this (sandwich) or
this (pizza). While not inexpensive, such a setup would be much more convenient for pizza making than a typical fridge. Auctions may be the best bet for finding one at a reasonable price.