The regulations actually don't require it. Under FAA rules for general aviation ("Part 91"), you need oxygen between 12,500 and 14,000 feet if you remain there for more than 30 minutes, and it's only once you climb above 14,000 feet that the pilot unequivocally has to have it. You need to get to 15,000 feet before the passengers have to have oxygen provided.
Additionally, a cold winter night means dense air which means more oxygen. As far as his lungs/brain are concerned, it's not 7,500 feet, it's more like 6,000 feet.
(More: http://www.faa.gov/pilots/safety/pilotsafetybrochures/media/...)