Unless you are willing to use a tripod (you can buy little mini ones that don't weigh much), it's too dark in the woods to take decent pictures without a flash. The faster film speeds are grainy, and you will probably be disappointed with the quality, especially with the ones you take in bright sun. "Pushing" the film (ie having it developed for a longer time) isn't the answer, especially if you are using colour films. They are designed to be developed a certain length of time at a certain temperature, and pushing will make the film unacceptably contrasty. You'd also have to pay double to have this done, and one-hour labs generally don't have the facilities to do it (I've spent time working in these places).
I used to be more into photography and took my SLR on my hikes, but then I broke down and got a point-and-shoot thing (but a good one, not a cheapo cruddy one). I never thought I'd say this, but I love it for hiking. It has its little built-in flash, so I can take pictures in the woods, it's waterproof, it's light and compact, has a zoom lens, macro, plus various other features that give you more control over the exposure. The picture quality is great, and many people have complimented me on some of my photos. I'll never go back to the SLR in the woods again unless I am on some serious photographic mission. However, if I were THAT serious about my photography, I'd bring a tripod. What I'm trying to say is, you aren't going to find a film that solves your problem - you'll have to either get a tripod (if you are trying to capture the natural light), bring a flash (if all you want is a snap of your companion standing on the trail) or forget about it, unfortunately.