Ash from wood fires is an organic material and can be disposed of in a number of ways.
It can be sprinkled on icy paths to act as a deicer.
It is high in nutrients (potassium carbonate, phosphate, iron, manganese, and copper) so can be added to soil as a fertiliser. However ash is highly alkaline and therefore should be used sparingly and with care in this manner.
Most plants like a slightly acidic soil, so adding ash may do more harm than good.
Ash’s best use is in soap making. You can turn your ash into lye water and then use this caustic solution together with oils (grow your own sunflowers?) and fragrances (grow lavender) to make completely homemade soaps.
At our house, the most regular use for wood ash is in cleaning windows. This was a method recommended by our chimney sweep. I was buying some nasty chemical cleaner to regularly clean the glass window at the front of our little wood burning stove. The stuff was expensive, not too effective and gave off nasty fumes. The sweep suggested that the ash from the fire itself is the best cleaning product for glass he had ever encountered. A ball of damp newspaper dipped in cold ash and rubbed on a window quickly produces a soap like layer that is fantastic for removing dirt. Rub the grey soap off with a dry newspaper ball for a smear free window that will be the envy of the neighbourhood. It is really quick and easy to do and there is no mess. This method doesn’t just produce great results (and the results really are first class) but saves on water and eliminates the need to use environmentally dmaging detergents. The newspaper balls can be thrown into the fire after use.