If the sun is closer to Earth in the winter, then why is it so cold? And if the sun is farther away in the summer, then why is it so warm?

If the sun’s rays hit the Earth straight on then it will be warm. This happens during the summer.

If the sun’s rays hit the Earth at an angle then the same amount of energy will be spread over a larger area and it will be colder. That is winter.

The change in distance between the seasons is relatively slight and thus has negligible effect on temperature.

The earth’s orbit is nearly circular, so the different is actually slight.

The effect @jerv mentions is also why the seasons are slightly harsher in the southern hemisphere—because both effects work together (the angle + the distance).

@jerv hit the main point. I wanted to add though:

The difference in distance is negligible. I believe the numbers are 92m and 94m (miles away). It’s ~2% difference. It’s not like we’re going between 30m and 90m.

The important bit to remember is that it’s not that the Earth is closer or further from the Sun (which it isn’t because the orbit doesn’t change that much), it’s the tilt of the Earth that results in @jerv‘s sun ray explanation.

and, the tilt of the earth means that during the winter the days are shorter and thus are warmed by the sun for a shorter period of time.

It’s not even so, if you’re in the southern hemisphere, where the warm and cold halves of the year are opposite. :-)

Right. If the top hemisphere is tilted towards the sun then the bottom half has to be away from it.

You’re in the wrong hemisphere, I’m afraid.

It’s all in the tilt. Our daylight hours change too, the closer you get to the poles. Right now, the northern hemisphere is tilted away from the sun, so we get less light hours and less direct light. The Southern Hemisphere is tilted towards the sun and experiences the opposite. There is a disparity, though, the Southern Hemisphere experiences it’s summer when we are closer to the sun. At 3 January we are approximately 91,500,000 miles away from the sun. At 3 July we are approximately 94,500,000 miles away. The variation in distance is only .33%, so that’s not really the issue. The issue is the tilt. If the orbit of the earth was more elliptical we wouldn’t be here. The orbit is more round than most solar systems in the Universe. .33% is really not that serious.

Yup, it’s all about the tilt.

http://www.loc.gov/rr/scitech/mysteries/seasons.html

Play with a flashlight pointing at a white wall. Change the angle and watch what happens.