Each kitty can have up to 9 traits. Traits counted are anything not genesis, and eye traits are Mysterious and Small. All starter kitties have genesis traits, and hidden traits. Those hidden traits can be new traits (as with any of the holiday starters) or they could be traits already discovered.
I suggest making yourself familiar with the Saga Charts...they list the traits in order from Dominante to Recessive.
http://sagakitty.blogspot.ca/
You can also go to the Manual tab at the top of the page and it will answer many questions on breeding and traits as well.
Welcome to KittyCats....your new addiction