The seasons are synchronized but they manifest differently depending on location. From what I've noticed in my game, weather tends to follow my sims around, when moving from neighbourhood to neighbourhood. If it rains somewhere then it will rain in the next neighbourhood, if it snows it will snow there too. I have seen snowing in Oasis Springs, but it doesn't accumulate on the ground. I took my sim to Oasis Springs to escape a blizzard and the blizzard followed her. You could possible use the weather machine to create whatever weather you want, but not sure how it works as I've never used it in my game. But I wouldn't worry too much about the different weather, you could pretend that Copperdale is higher up on the mountain and it snows there.
