I ride a mtn bike. I bought one about a year ago and decided that's about the most fun a person can have and stay out of jail. I'm like a little kid when I'm on my mtn bike. A couple months ago I bought a road bike, mostly to ride and stay in shape when time constraints are such that I can't load up my mtn bike and drive to the trails. Holy cow I'm loving my road bike just as much. So I've logged only a few rides the last few months on the mtn bike but have put over 1000 miles on the road bike. The mtn bike rides are usually on gravel and fairly smooth or otherwise not technical single track. Yesterday we went to a trail we ride a couple times a year that is a long lung bursting climb to the top with a long, fast and technical descent. As I was going down I became a bit tentative thinking I was in some real danger of getting injured, especially crossing sections of rockarmor trail. All I could think was, "If I break my collarbone I won't be riding ANY bike for a while." At age 55, I know I won't heal as fast as I would in my younger days.
So I guess my point is, I don't typically feel danger on my road bike, or even my mtn bike for that matter usually. But there are certainly trails that are more technically and physically challenging than others, and just faster. Thus by default, the danger level can go up. Judge your trails according to level of danger, risk or adrenaline rush you're willing to accept and then go ride your bikes according to your own set criteria. Ride your own ride and don't worry about how you look or how fast you go. Mountain bikes are great fun and safe as road bikes. Road bikes are great fun and safe as mountain bikes.
One thing to consider, you'll never be hit by a distracted motorist texting out in the woods. That's probably the greatest element of danger we face on road bikes, and a very real one with likely worse outcomes than falling on the trail.
Couple hints, use both brakes when descending a steep slope, always keeping one or two fingers on the levers. Trying to slowly and tentatively pick your way across rocky/rooty/technical sections will likely cause you to crash. Keeping up some speed will actually help float across the rocky sections. It's amazing the terrain today's mountain bikes can take. Drop your seat on the downhills and literally push your butt off and behind/below the seat on really steep downhills and use your legs/knees along with your suspension to absorb shock. Try not to hold a death grip on the handlebars, that's likely where your sore wrists/fingers are coming from. Have fun!