As far as celestial sphere is concerned, I think we can assume that it mirrors our own, but with a few differences...
Jon IV, Storm 30
The colors are just a description of the sunrise and a reminder that we are in autumn. The more interesting thing here is the Sword of the Morning constellation on the southern horizon, as seen north of the Wall. Forget for the moment that a 700-foot wall of ice should have blotted out the southern horizon from the view of a man (even if he is the special snowflake) standing on the ground just north of the Wall. Rather, concentrate on the shape of the constellation and the bright white star in its hilt blazing like a diamond in the dawn. It should be a cross with a very bright star at one end. Well, that is Crux, also known as the Southern Cross. The Southern Cross, of course, is a small, cross-shaped constellation, with a first-magnitude star (the brightest stars in the night sky), at its bottom end, called Alpha Crucis, also known as Acrux. The analogy is not perfect though. Acrux is at the end that would be the point of the sword, and in any event, it is a blue star. Gamma Crucis, also known as Gacrux is the star that would be the sword’s hilt, and Gacrux is red. The other problem is that the Southern Cross is not observable from north of the 26th parallel (South Florida).
That an ASOIAF constellation resembles one of our own should not be surprising since several celestial bodies described in ASOIAF mirror our own. The George had just given us a little more astronomy in Jon’s preceding chapter in Storm. . .
Jon III, Storm 26
The twelve houses of heaven correspond to the zodiac; the seven wanders correspond to the classical planets of antiquity (i.e., the Sun and Moon and the five planets visible to the naked eye, Mercury, Venus, Mars, Jupiter, and Saturn), and the red wanderer corresponds to Mars. The Moonmaid most likely corresponds to Virgo since there is a whole bunch of astrology mumbo jumbo about when Mars is in Virgo.
The first mention of an “ice dragon” follows Bran’s realization that the old powers are real. He then asks Osha how to go north, and what he might find. Osha tells him to look for the Ice Dragon, and to chase the blue star in the rider's eye. (It should be noted that after this mention as the blue star in the rider’s eye, it is afterward referred to as the blue star in the dragon’s eye. Since Jon tells us later that the Wildings’s nomenclature for celestial bodies is slightly different than the nomenclature used south of the Wall, this is not necessarily an inconsistency.)
Thus, we learn that the Ice Dragon is a constellation, and that the blue star in the dragon’s eye is a pole star. Currently (more on that in a moment), the north pole star in our sky is Polaris in the constellation Ursa Minor, also known as the Little Dipper. Thus, it appears that the star in the dragon’s eye that points north corresponds to Polaris. But there are differences here too. Polaris is more white than blue, and Ursa Minor is a little bear, not a dragon. However, Ursa Minor is bordered by Draco, which is a dragon, in the north sky, and one of the stars in Draco is Thuban, which is more blue than white.
Now, here’s where it gets interesting (whether the George intended it or not): The Southern Cross was visible from the British Isles, Canada, Alaska, and Russia 10,000 years ago, and it will be visible from those regions again after another 15,000 years. This is due to the motion of the Earth called axial precession. This is the motion you see in a wobbling top as it starts to slow. The Earth’s axial precession takes about 26,000 years to complete.
Due to this axial precession, the north star 6,000 years ago was Thuban, a blue star in Draco! And while you might not have been able to see Acrux from Scotland 6,000 years ago, you would have been able to see it from England.