Is there any dynamical reason for the winter solstice to happen close to the perihelion? When the winter solstice arrives, the angular momentum of the Earth, its orbital angular momentum and its radius vector with the orbital focus in the Sun are in the same plane. This happens quite close to the perihelion (~2 weeks later), where both the orbital angular speed of the Earth and the curvature of the ellipse are at its maximum.
Is there any dynamical relationship for the major axis of our orbit to follow the direction of the rotational axis of the Earth, or it is just a coincidence and the perihelion could well be in, say, april? 
EDIT: Yes, there is no observed resonance between the precession of the Earth ellipse and the Equinox precession (+1 for both answers and, thanks!). But the question goes in another direction. Perhaps there could be some tidal forces near the perihelion, related to the departures from the rigid solid model because the molten interior of the Earth, so that there could be some form of weak transference of momentum from proper to orbital (in analogy with the transference of momentum with the Moon, that nowadays slows down the Earth rotation and enlarges the mean distance to the Moon).
Has anybody developed that question analytically?
 A: I think it is basically a coincidence at the current time.  Earth's axis of rotation precesses with a period of about 26,000 years, and according to Wikipedia, its orbital axis precesses with a period of about 112,000 years.  So the winter solstice and perihelion will have all possible relative phases over a long time period.
A: Around 4080 BC the Earth was in perihelion during autumn. In 1246 AD the perihelion occurred during the winter solstice. By 6427 AD the perihelion will coincide with the March equinox. Perihelion will occur in April around 7062 AD. (source: Astronomical Algorithms)
The question is: Is the Earth's lunisolar precession coupled to its perihelion precession? Or, to put it another way: Does the Earth exhibit 1:1 (synchronous) precession-orbit resonance?
The answer is, it doesn't. The only known example of precession-orbit resonance is the Pluto-Charon system.
A: Answer to your old question:
Right now, the perihelion currently occurs around the same time as (2 weeks after) the northern winter solstice, but 10000 years from now it will occur around the northern summer solstice.   So, like other people have said, it's just coincidence that right now they both happen at about the same time.
Answer to your new question:
This is one of my favorite video series on the earth's orbital cycles
video #6 and the remaining 2 videos will give you a good grasp of aspidal (perihelion) precession.
Although I personally do not know which one affects which, earth's many orbital cycles are heavily influences by the following factors:


*

*the earth has an equatorial bulge (43km fatter than it is taller)

*the sun's gravity

*the moon's orbit/gravity

*saturn's/jupiter's orbit/gravity


and account for changes in:
Obliquity (tilt of the the earth) - Currently, the earth's axis is tilted at about 23.44° in relation to it's orbital plane. But over a period of about 41,000 years, it oscillates between a tilt of 22.1° and 24.5° and back again.
Eccentricity (shape of the orbit) - Over many years, the shape of the earth's orbit will change from more elliptical to more circular and back again. Primarily due to interactions with the gravitational fields of Jupiter and Saturn, the eccentricity cycles are somewhat erratic and it's terms vary between 95,000 and 125,000 years (with a beat period 400,000 years), and loosely combine into a 100,000-year cycle.
Precession (position of the orbit) - The direction of the earth's tilt with respect to background stars will cycle every 26,000 years.  The northern winter solstice and perihelion will coincide every 21,000 years.  And the perihelion will coincide with background stars every 130,000 years.
