When I was a teenager, my family would go into the High Uintahs camping every year. We went 11 miles and from about 7000 feet to 1000 feet in altitude. Our basenji "Bell" always had a great time hiking with us. We would usually hike up on a monday starting out at around 8am and arriving at our destination around 2-3pm. We usually stayed the week and made the return trip on Saturday. After arriving we would usually hike to one of the several lakes in the vicinity. Bell always had a great time! She was pretty much off-lead the whole time and would stay right with us, sometimes venturing just a little off the trail - but we would whistle for her periodically and she would come running. With all of the extra running that Bell did on the hike she was tired at the end of the day, but she was ready at any moment to do some more! Bell went up to the mountains with us many times and we never had a problem with her - she was off leash pretty much the whole week.
I do a bit of hiking in the canyons nearby in the summer and my current B Samantha loves it! She'll go off to investigate something occasionally, but if she gets out of sight, we just whistle for her and she comes running back to join us.
We took Samantha camping soon after we got her (she was 4-1/2 years old at the time) and I got up to get her out to do her business early one morning. We hiked up a trail a nd were about a quarter mile away from the campground (we were in one of the campsites at the edge). I let her off lead since she had stayed pretty close to me when off lead in the forest before. This time she saw or heard something in the forest and took off running. I waited for 5 minutes or so whistling and calling her name and didn't see her. As I started hiking up the hill that the trail ran along, I saw her come running back down toward the trail to one side of me. I ran back to the trail and called her again, but no sight of her. I walked up and down the trail looking and finally decided to go back to camp to get my wife and kids to help me look for her - and there she was sitting at the door of the tent waiting for me - looking like: "Hey, where have you been - I'm cold and want to go back in the tent!" I was amazed at her sense of direction and loyalty to me after only a couple of weeks.
My first basenji Bell did kill a deer that got into my dads orchard (how it got into an area with a 10' fence I'll never know), and I have heard stories that B's have been killed by coyotes, so you have to keep an eye on them out in the wild - probably no different than any other dog though. And if you have a lot of rattlesnakes around you might want to check out an article in Basenji magazine (September 2007 issue?) about de-snaking them.
B's do make great trail dogs, and it sounds like your the active type that would be right for them. They do need daily exercise. There's a saying that I wholeheartedly subscribe to: "A good Basenji is a tired Basenji!". I'm doing better in that department than I've ever done with my other two B's, and Samantha is my best B yet - I think it's because of the amount of time that we get out walking with her. When they know their going to get exercise they are much better behaved and more patient with you when you have a busy day and can't get out on the usual schedule.
By the way, B's do love to snuggle in bed, or up next to you on the couch. The things that I love about them the most are the sounds they make and the sounds they don't make, the lack of drool, and the nice warm soft a slightly moist tongue (when they lick you you don't feel like you've been licked by a dog!). I love to watch them run, and I love the way they play with you. I love their curly tails! They are a dog with personality - you'll definitely be entertained! I love the short hair and the way they don't smell like a dog, but they do shed a little and those short hairs don't always come of the couch with the vacuum - we have to use duct tape!
This is my favorite picture of Samantha hiking in the canyon!