I'd say it all depends on which country you are living in, your support system, the amount of sun/heat/light you get every day and how content you are with your life.
Firstly, if you live in a country that is stable, and offers you good support (be it education, living conditions, wages etc.), you will automatically feel more rested, regardless of the season. Knowing that you have a support system (which not only comes down to the country, but also your personal support system; family and friends), will naturally make you feel less stressed. But this doesn't really answer your question, does it? (My apologies.)
However, it has been clinically proven that the amount of sun we get reflects our mood. We all dream of our vacation days, summer, sun and the beach (unless you're the outdoorsy, Mount Everest climbing type) and relaxing. It's funny how we associate heat and sun with calm and serenity. And I suppose that is part of why we enjoy summer so much. It gives us "light" and it makes us all loosen up, take our clothes off and, effectively, "let our hair down".
Whereas the winter is dark, and somewhat depressing as people (much like animals) go into their dark cave and brood in the warmth of their bed.
And finally, I believe - without any proof whatsoever- that a person will be happy no matter what the season, if they are content with their life and the people in it.
Also, love never hurts right?
Allie is right, it has been proven that the more vitamin D (the nutrient we get from the sun) we receive affects our mood, due to vitamin D increasing serotonin levels in our body.
However there is more to this. The body has a natural body clock to wake up when the sun streams through your window, and it begins to shut down when the sky's begin to darken. If you take into consideration where you live and the fact that in the winter the nights are longer, when the alarm goes off at 6am and it is still dark you do not want to get up, however in the summer when the sun rises earlier it does not seem that much of an effort.
The science behind this involves melatonin and serotonin, two neurotransmitters in the brain. Melatonin is produced when we sleep. Sleeping too much produces abnormal levels of melatonin. The more we sleep, the more we want to sleep because of the increase in this neurotransmitter.
On top of that in winter sunlight is in short supply, our serotonin levels drop and we do not have much energy or so many good feelings.
There are devices called dawn simulators which help people to get moving in the morning. They work like the sun rising and gradually increase their light density until it is time for you to wake up. This will trigger you to wake up even though it is dark outside.So if you find yourself getting sleepy during the winter months, maybe going for a walk during your lunch hour may help to boost your serotonin levels, lift your mood and give you that little bit of energy you need.
It depends on the weather and how can we organize the 4 seasons, but actually we do more activities in the warm weather and in the Summer,otherwise, if in the cold season, people can do some activities of skiing and others in door activities too, on the conclusion, the cold weather make us rest as there are few activities.