Is it true that distance between earth and sun is closer in winter season (January) and farther in summer season in the Northern Hemisphere?
Yes, it's true (in the northern hemisphere). The small eccentricity of the Earth's orbit is not anywhere close to a key driver in the seasons. The key driver of the seasons is the Earth's obliquity. In the northern hemisphere, the axial tilt of Earth's rotation axis has the northern half of the Earth facing a bit toward the Sun in June/July/August and away from the Sun in December/January/February. The opposite is true in the southern hemisphere.

Eccentricity would be a driver of the seasons if the Earth's rotation and orbital axes were much closer in line with one another than they are. If that were the case, summer and winter would be world-wide phenomena. As it stands, when its summertime in the northern hemisphere its wintertime in the southern hemisphere, and vice versa.

Somewhat paradoxically, even though the Earth is closest to the Sun in early January and furthest from the Sun in early July, the Earth as a whole is cooler during December/January/February than it is during June/July/August. The reason is the uneven distribution of land and ocean between the northern and southern hemispheres.

In 13000 years, northern hemisphere summers will occur near perihelion passage and winters near aphelion passage. Those will be brutal times! Fortunately, I won't be around to see them.