The problem lies with your camera's light meter. It is designed to measure the light and set the exposure for an average scene, and under average conditions it will normally do a very good job. This is because an average scene has an unusual property; it reflects approximately 18 percent of the light falling on it, equivalent to a mid-tone grey. It doesn't matter if it's a landscape of rolling fields, a city street or your own living room, the average amount of light reflected is always around that magic 18 percent figure. Your camera's light meter is calibrated to take account of this fact, which is why it will produce the correct exposure in any normal situation. In fact professional photographers will often use a special 18-percent grey card to help make very accurate exposures. They will have their model hold the card, or place it in the scene to be photographed, and take a spot meter reading from the card.
However good your light meter is though, it will start to have problems whenever it tries to measure a scene where the light reflection is different from the average, and snow scenes are a prime example. The white snow reflects much more than the usual 18 percent of available light, but your camera meter doesn't know this. It measures the light using its 18-percent calibration, and the result is a large degree of under-exposure. We can demonstrate this effect with this handy indoor simulated snow scene. The grey-scale panel is taken from my tutorial on exposure metering, where I explain the Zone system.
As you can see, the light meter has measured the light reflected by the scene, and has assumed that it is supposed to be the usual 18 percent. As a result, what was supposed to be white has come out as a mid-tone grey, and the two chess pieces standing in for skiiers or snowman-builders are very under-exposed. We can correct this to some extent by the using exposure compensation feature found on all digital cameras. By adjusting it to +2 we increase the exposure and the brightness of the image, restoring the white background to white, and ensuring that our subjects are now correctly exposed.
Increasing the exposure does have two potential drawbacks however. First, it usually means using a much longer shutter speed, which increases the risk of camera shake. If your camera has image stabilisation make sure it's switched on, and if you have a tripod or monopod, use it. The second problem is that of over-exposure, which could result in the white snow being completely burned out, leaving a plain featureless area of white in your picture. This is always a risk with snow photography, so if your camera has exposure bracketing it is a good idea to make use of it.
Another good way to avoid this problem is to use spot metering, if your camera has this feature. It is a little more complicated to use than the normal multi-zone metering, but the results will often be much better. For most cameras, the way to use spot metering is to aim the centre-spot of the frame at the subject's face, half-press the shutter button to take a light reading, and then keeping button half pressed, compose your picture and take the shot.