Ive read (i dont remember the source) that if there are no AGENDA cards in play the game is in SUMMER (default season, is this correct?) , but the attachment card, Crown of Winter says: .Attached character gets +2 STR and is immune to opponent's events and character abilities. If the Black Raven card is not in play, it is Winter.

Q: If the black raven is not in play and also no other agenda in play, What season is it? summer or winter? is my information correct about if there are no Agenda Cards in play it is summer by default?

Khalpongo said:

There are currently no agendas that affect the seasons (there will be two in the Kingsroad cycle). There is also no default season - it is not summer by default.

It is only summer if a card (eg Crown of Azhor Ahai, Black Raven, Crown of Mereen) makes it so, and it is only Winter if a card (White Raven, Crown of Azhor Ahai, Crown of Winter, Cotter Pyke) makes it so. The seasons are not mutually exclusive. You could have it be both Winter and Summer with, say Crown of Mereen and Cotter Pyke in play.

Lastly, there is no effect of their being a season except what is written on the cards themselves.