If you were shooting in Auto (Program) mode, the camera was selecting the optimum shutter speed and f/stop based on your ISO setting and the camera's internal metering calibrations.
To understand why the snow came out too dark, you have to understand two basic aspects of photographic theory.
First is what is known as the gray scale, which is a ten step scale of b/w tones that go from pure black to pure white. "Middle Gray", or Zone 5, is what EVERY light meter sees without respect to the subject matter. When you shoot in Auto mode, your meter is recording the snow as a middle gray. But in reality, snow (with detail) is between Zone 7 and Zone 8 (Zone 10 is pure white).
Second is understanding how light itsself works. The sun is a constant light source that nevers varies its distance from our planet. When this light strikes a black object we want it to look black in our photographs. The same is true for gray and white objects - we want them to record that way. If you underexpose white subjects they look gray. If you overexpose black objects they look gray. If you overexpose gray subjects they look white and if you underexpose them they look black.
When you shoot in color, these principals hold true to an extent that lets you apply them for your exposure. Since white snow fits on the gray scale at Zone 7 to Zone 8, you have to increase your exposure between 2-3 stops to make the snow look white when you use the camera on manual mode (in otherwords, you have to override what the meter thinks is the right exposure). Too many people think that digital cameras and auto modes will always give you outstanding results, which just isn't true.
The person using the camera has to know when to be in control of the shoot and reject the computer programming decision being made in the machine.
If you want to understand this principal, buy a set of three 11x14 mount boards - one black, one middle gray and one white. Tape them together black-gray-white and have someone hold them at mid-chest level. Shoot a series of exposures at 1/2 f/stop intervals from your smallest to largest aperature at the same shutter speed. Compare the images on your computer monitor to evaluate what happens to the three basic tonal values at each of the different exposures. Keep a log as to which frame is shot at what aperature.
Now you should understand exposure and gray scale values.
Michael