Why is winter colder since that's the time the sun is closest to earth here in the northern hemisphere?

The difference in distance from the Earth to the Sun between winter and summer is not great enough to enduce seasons on Earth. Seasons occur because the earth is tilted on its axis relative to its orbit around the Sun. Where the tilt faces the Sun summer occurs. As it turns out, the southern hemisphere is tilted toward the Sun when Earth is closest to it, and the northern hemisphere is tilted toward the Sun when the Earth is farthest from it.