How wet has it been where you live and is where the Cordy have good drainage?

it's been fairly wet,and the tree is at the bottom of a slopy garden, not the best drainage but not the worst either.

Normally I would say it sounds like frost damage (they are not that hardy) but I though Cork rarely got hard frost and is mild if wet. I would fork gently around the roots to aerate it, removing any grass or plants near the roots to stop competition for nutrients (the pale green colour could mean lack of nutrients) and then feed it in spring. Am guessing it is pretty big (above 1.5 metres?) with your climate and not something bought for a few Euro this year in a 1 litre pot? If it is the latter then I would move it to an area with better drainage. If it is too big to move then improving drainage and a feed in spring and throughout summer will perk it up. Judging by the Cordy's in the UK, they are root hardy (a lot were wiped out in the severe winter of 2009 and 2010) but re-emerge slowly in summer.

thanks for that! will do everything you said and let you know in the summer if it's revived.