The imagery of seasons plays a prominent symbolic role in A Clash of Kings. In the Seven Kingdoms, summer is equal to love, gentleness, bounty, and life, while winter amounts to hate, harshness, famine, and death. That's not much different than the symbolic roles these seasons play in countless other novels, plays, and poems.
The only real difference is that a Westeros winter or summer could last ten years. There are hints in the novel of winters that lasted an entire generation. Even given the ridiculous death rate of people in Westeros, that's got to be like, what—forty years? So the seasons may represent the typical fare, but for the people of the Seven Kingdoms, the magnitude of the symbolism is much greater. The seasons are big, and so, too, what they represent.
For example, during Renly's feast, Catelyn thinks to herself, "Winter comes for all of us. […] For me it came when Ned died. It will come for you too, [Brienne], and sooner than you like" (23.Catelyn.109). Here, she doesn't mean that an unpleasant time will come for Brienne, but it'll be over soon, say, three months from now—she means that a truly horrible time will come for Brienne, something so bad that it will either kill her or devastate her world possibly for the rest of her life. Winter's no joke in Westeros.
Similarly, Brienne proclaims, "Winter will never come for the likes of us. Should we die in battle, they will surely sing of us, and it's always summer in the songs. In the songs all knights are gallant, all maids are beautiful, and the sun is always shining" (23.Catelyn.108). Summer is associated with all things good and wonderful: gallant gentlemen, beautiful women, and sunshiny days. Brienne's description of the songs almost sounds like a heavenly afterlife, and this correlation between heavenly imagery and summer shows just how important this season is for the Seven Kingdoms.
Also consider that their technology is stuck in the Middle Ages. This means that winter is a more dangerous time for them. So rather than worrying over a spike in the power bill because their apartments run on baseboard heating, these people need to worry about not starving to death because they didn't save enough crops to last a decade, or can't hunt down enough deer.
So when Bran proclaims to Jojen and Meera, "May your winters be short and your summers bountiful" (22.Bran.37), that's basically the nicest thing you can say to someone from Westeros.