Sorry for your loss. As the worst storms for twenty odd years, all the barely-standing-up half dead stuff thats stayed up has come down in the last couple of months, so you've got 20 years worth of dead wood coming down at once- not every year will be like this.
To try and put a positive on it, sweet chestnut is great timber. Its very weather resistant and attractive. Consider turning some of it into either shingles or buying a mobile mill and planking it; it splits easily and would be useful for outdoor uses. Where there's new light, new stuff will spring up in a couple of years- you'll be surprised at the regrowth, its part of a cycle.
Don't let it get you down, but it is unfortunate timing after your recent purchase. Springs coming, and its a wonderful time in a wood.
