Last year we had a wood-stove fitted in the house, and over last winter I collected all the ash into a large plastic drum (when it was cold, of course!). All the wood we burned was untreated raw timber direct from the tree itself. This year, as I was digging over the beds for winter, I tipped the whole drum onto one bed and mixed it in, to see if it makes any difference when compared with the other bed's crop next year.
I have absolutely no idea what the outcome will be, or whether I've done the right thing in the first place. But let's just call it an experiment, and I'm sure lessons will be learned from it.