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.