I used wood as my primary heat source for 20 years and learned as a kid what to do right. Never had an accident or really even a close call. Worst thing happened was while dressing a chain I ran the file across my thumb and put a dent in the nail.

Me, closest was a saw that ended up hitting a chain saw chap working on a tree on a very steep hill. Cut it a bit, but nothing serious which is why one wears them. I cut trees full time 180 days per year. Now if you asked about trees that didn't go where I want that would be a different story. I am also on the local FD and I have taken any number of people who didn't have the correct PPE to the hospital, some in pretty serious shape. But in any case if you cut trees you need boots, chaps, jacket/overgarment with PPE built in, helmet, ear and eye protection. That's pretty much what you can do.

Years back I was limbing a downed tree and a good sized branch bent backwards and sent the saw to the ground right where my foot was. So glad I always wear steel toed boots. It cut through the tip of my boot and you could see the steel as plain as day. No damage to me but I called it a day nonetheless.