Earth's perihelion vs winter solstice
There is no connection between the date of the solstice and the perihelion. It is merely a minor coincidence that perihelion occurs close to the solstice. 

The relationship isn't fixed. Precession in the Earth's orbit (caused by gravitational perturbations of Jupiter and other planets) will change the relative time of perihelion and solstice over a period of thousands of years.