RRD, you've received great suggestions already, so I have just one thing to add. My family is very active and enjoys the out of doors immensely. My kids are older than yours now, and we live in huge wild animal country
When my kids were younger, one of my dds in particular was freaked out by two of the types of large animals that live around here (and sometimes show up in our yard).
Have you talked to your ds to attempt to figure out the source of his fears? Is it just a general childhood fear, or is it possible he's heard reports of people being injured by bears? Or do kids where you live get instructions on what to do if lost in the woods or how to react if they encounter a bear? Does your family wear bear bells or purposely make noise when skiing or hiking in bear country? Have you seen bears etc on trails when you've been out together? These were all things that helped lead to my dd being completely freaked out - but if you know that they've scared your child you can talk about it and turn the conversation around to how to prepare and avoid trouble with bears.
My other small piece of advice is patience. I had no idea at your ds' age what my childrens' favorite activities would be that would take them into their teens and adult years, but fwiw, the one that turned into an avid skier and mountain biker is also the kid who was scared to death of the big wild animals. She is still scared silly by them, but she loves to bike and ski so much that while she's actively doing so, she doesn't worry about the other. It took a few more years than where you're at though, with a lot of talks about the logic of her fears, how to protect herself, and the relative risk of injury from a wild animal, for her to get to that point. If we'd pushed her, I think it might have backfired.
One thing that may have helped was that she participated in local children's groups for both skiing and mountain biking (groups that were very large - over 100 kids in each, skiing and biking 2-3 times per week). What was scary with our family was a bit less scary when shared with lots of people she didn't know as well
and with other kids she did know who she knew she'd have fun with
She *did* run into large wild animals on several occasions over the years with these groups, but didn't freak out in response, and learned how to deal with the situations through having adults other than mom and dad lead her and the group of kids through what to do.
Best wishes,
polarbear
