You could also try a graduated neutral density filter.
Using a graduated neutral density filter is usually my method of choice when trying to balance photographs that include both the forest floor and the sky coming through the canopy. Although it's far from perfect, I feel that this provides the best compensation overall for the wide dynamic range of such shots.
Polarizers are an option of course, and I occasionally give them a shot in certain situations. Despite darkening the sky and deepening its saturation, though, it is only under rare circumstances that this effect proves potent enough to counteract the disparity between the dark forest floor and bright sky.
HDR seems to be the obvious go-to technique, but in my experience, it too is only useful under very specific conditions... even less often than the polarizer. If there is even the slightest breeze coming through the forest, then I generally don't even bother bracketing my exposures... I already know that an HDR result will be sub-standard. The problem is that I almost always use very small apertures for my landscape photography -between f/18 and f/32- and this can make for some rather slow shutter speeds. If the trees in my shot are bouncing around ever so slightly in the breeze, then three merged exposures of the same scene will nonetheless produce a canopy that lacks sharpness and exhibits ugly ghosting artifacts in the branches.
Ultimately, the graduated neutral density filter remains my most reliable option under most conditions when taking shots from the forest floor that include bright sky. The downside? The grad ND will darken
everything that it covers. Although it will produce less blown-out skies and offers a wide range of positioning options, it does this at the cost of darkening trees and leaves in a slightly unnatural-looking way. With a bit of finesse in post-processing, though, some this can be remedied to produce an excellent photograph nonetheless.
Shots from the forest floor are tough, in general. The best aren't necessarily produced exclusively by exceptional technique alone. Rather, they are the result of rare alignments of ideal conditions which a savvy photographer stumbles upon from time to time. In all other situations, one can only use experimentation and experience to decide which option -grad ND, polarizer, or HDR- will offer the best compromise and produce the best photograph. "Compromise" is the key word here, though...