Two things about the CRV: First off the "real time" 4wd is also known as "on demand." What this means is that the rear wheels don't start getting power until the front wheels are spinning. IMO this is too late to be engaging the rear wheels and it's one of the reasons we crossed the CRV off our list when we went shopping for a new vehicle for the GF. The salesperson also said something about the 4wd not kicking in over 40mph but I don't know about that. She was actually a Subaru salesperson so she may have been trying to steer us towards the Forester, but in any case, don't count too much on the "4wd" of the CR-V.
Second thing: Before taking a CRV onto anything other than a well graded road, take a good look at the underside: The gas tank hangs real low off the center-left of the vehicle, in fact, it's one of the lowest parts of the undercarriage (the Element, which I almost considered getting, has the same problem.) It is protected by a tubular skid plate but that's a pretty important asset. Putting a skid plate on it would reduce clearance even more.
I actually followed a CRV for a couple of miles in the Maze District of Canyonlands last month, and I expected to see him high-center any minute. Fortunately he found a parking place at the trailhead a couple of miles from the Hans Flat Ranger station and parked there. If he'd gone any farther I think he would have been in real trouble. There are trails there that a vehicle like the CR-V could get down, but getting back up without a winch would be virtually impossible.