Note the tilt does not bring the Earth significantly closer or further away from the Sun! The angle is the important part, not the distance.
The Earth's orbit is almost (but not quite) a perfect circle. It is only slightly elliptical.
The Earth is also closest to the Sun in January, so distance cannot be the reason it’s cold in the winter in the Northern Hemisphere. If the distance determined the seasons, we would also not have opposite seasons in the Northern and Southern Hemispheres. (6/)