You may see me in 7 if it's your time
Though you will probably see me in 6 all around town
Some say my predecessor can hold up the world
In the west I am a group of siblings in a cow
Though in the east, a furry skull house in an achromatic cat
What am I?
All right, I decided to flesh this out into the full answer... You are:
The seven sisters of the Pleiades
You may see me in 7 if it's your time
In the Winter, with good eyesight, you may count all seven. This requires, of course, a clear night, as well as allowing your eyes to become accustomed to darker light to see the dimmest of the seven stars. Furthermore, in November, the stars remain visible from sunset to sunrise.
Though you will probably see me in 6 all around town
The Subaru logo is of the constellation Pleiades (Subaru is the Japanese word for Pleiades) but only has 6 stars in it. You will likely see a Subaru car when you go anywhere
Alternate explanation (not intended meaning): In town, bright light will make it hard to see all 7. Most cultures refer to the 7th sister as being missing, forced to sit in the back, or have some other explanation as to why only 6 are (easily) visible.
Some say my predecessor can hold up the world
As Eutherpy notes, they are the offspring of Atlas, who holds up the world.
In the west I am a group of siblings in a cow
Those 7 stars form the seven sisters (siblings) of the Pleiades (in Taurus, the cow) in Western astronomy.
Though in the east, a furry skull house in an achromatic cat
In Chinese astronomy, there is a group of stars that forms the White tiger of the West (achromatic cat). Seven of those stars form the 昴 (translated to hairy head). Groups of the stars are translated (again, according to the Wiki linked) as a mansion. Thus, achromatic cat's furry skull house.
And of course, there's the title
Horoscope relates to astronomy
What comes to mind is:
Taurus (the constellation)
The "cow" reference is pretty obvious. It also fits in with the title hint
(horoscope)
and the "group of siblings" might be referring to
Pleiades/Hyades.
You might see it only at a certain time - "if it's your time", i.e.
if you're, for example, in the Northern hemisphere's winter or spring... although 6 a.m. seems to be a bit too late.
Edit:
I believe it's not the entire constellation, rather a group of stars (as Ivo noted in the comments) - either the Pleiades or the Hyades, since in Greek mythology, they are the children of Atlas, a titan condemned to hold up the sky ("Some say my predecessor can hold up the world").
You're
Pleiades
You may see me in 7 if it's your time
Though you will probably see me in 6 all around town
The seven most prominent stars in this cluster [Pleiades] are at least visual magnitude six, and so the cluster is also named the "Seven Sisters" - via the Wikipedia article on Taurus
Some say my predecessor can hold up the world
Parents of Pleiades are Atlas and Pleione.
In the west I am a group of siblings in a cow
Though in the east, a furry skull house in an achromatic cat
Couldn't pin these last two down for Taurus or Pleiades, though I'm confident it's the latter...
