If Hawaii equals surfing then Mammoth equals snowboarding. What some would call surfing on snow, snowboarding is probably the prime reason people go to Mammoth in the winter. Though they are the exact opposite in terms of climate the two regions are tied together by one sport...surfing...even if one is done on water and the other snow.
Mammoth reminds me more of the North Pacific Coast region than the California region because of its snow capped mountains and the beauty and bounty of landscapes. It is also somewhat isolated from the rest of the state much like the North Pacific Coast is isolated from the rest of the country. In the winter time many of the west to east passes are closed due to snow. The forests of Mammoth also remind me a lot of the North Pacific Coast region.
Mammoth Lakes is just about right in the middle of California on the eastern edge. When most people think of California they think beaches and Hollywood. Mammoth shows the states diversity. The state has the best of all worlds. It has great beaches in San Diego, great cities like San Francisco and great mountain and wilderness areas like Mammoth. 
The Paiute Indian tribe were one of the first group of people to populate the Mammoth Lakes region. Though it does not have much of a Southwest Border feel to the town, aside from your standard Mexican food restaurant, it does have a deep history of Indian culture. Take anyone of the guided tours and you will hear about the first people to navigate these canyons.
Mammoth Lakes could be considered the Empty Interior of California. It has large areas of sparse population, variations in topography and economic activities unevenly distributed and widely scattered. This is probably the reason many Californians visit here during the year...to get away from their busy lifestyles and enjoy the emptiness.
