there are more problems associated with digital such as white and color balance that I'm not very familiar with. I'd read up on those to understand a little more about your brightness problem. I'm sure your camera has white balance settings etc.
You are right that bracketing actually takes ALL of the 3 or 5 photos for the 5 different exposures. In certain photography situations you can do this (photo of castle for example) but can be more difficult for moving subjects such as climbers.
Aiming your camera at the sky also works for 35mm cameras. The light meter reads whatever you point it at. It measures the amount of light reflected off something. If you aim at the sky you will expose the film for that amount of light which means you will have underexposure climbers if you then turn it on them and take the photo for the same exposure. I'm surprised you haven't had that problem. A perfect example of this is trying to get silhouette shots. If you want to achieve this type of photo, simply face the sun, set your exposure while metering off the bright blue sky looking at the light, then introduce a climber and take the photo. Here is an attempt at explaining that a little more clearly. When you look directly at the sky, the camera sees a lot of light and tells you to shut the appature (like a squinting eye) so that you don't overexpose the film because there is a lot of light. However, when you introduce a subject in front, their back which is turned away from the sun, reflects very little light. Thus there is not enough light or a long enough exposure to properly expose the climber which results in a black silhouette with a bright blue sky. Try it next time you are out.
Remember that every photo has a real/correct exposure. The trick is finding it. Bracketing is a way of making sure you hit that perfect exposure.
Mitch, can you set appature and shutter speed on your camera? If yes here's what I suggest you try next time. Instead of aiming at the sky, try aiming at things that reflect the light from the same side of the subject as the photo you want to take. For example, if you want to take a photo of the front of the house that is in the sun don't meter off the back of the house but instead meter of the front of the house. If the house was white and filled the full frame a trick that photographers might use is to look at the front of the house, put their hand up and meter off the back of their hand. They also sell 18% grey cards to do this. It's not perfect but usually give you decent results when you are in a tricky situation like at the ski hill or in front of a big black boulder.
does this make sense?