Earth is closest to the Sun in January. So why is that winter?

Summer can't be caused by being closer to the Sun: Earth makes its closest pass around 3 January and is farthest around 4 July. The distance changes by only about 3%, worth roughly 7% more sunlight.

The real driver is Earth's 23.4° tilt. Leaning towards the Sun lifts it higher in the sky and stretches the day, so at 50° north a square metre gets more than five times as much sunlight in June as in December. Drag Earth around its orbit and switch the tilt off to see the seasons vanish.