Fading is caused by ultra-violet radiation in sunlight. The atmosphere tends to filter out this UV radiation. Much more is filtered out in winter, since the low sun means the slanting sunlight has had to pass through much more atmosphere before it reaches us.
In summer, a UV Solar Index of 7 or 8 would mean rubbing on the suncream. But in winter the Solar Index is more likely to be 1 or 2, where protection is un-necessary.
You're right about reflection from snow - but this tends to be more of a problem in high mountainous areas where the air is so much clearer, and less of the UV is blocked.