If someone has a cold sore that cold sore is highly contagious to anyone coming into contact with the cold sore.
The cold sore stays contagious until the cold sore is entirely gone even when the cold sore is scabbed over.
Never kiss someone who has a cold sore unless you want to catch a cold sore too.
Cold sores are caused by the herpes simplex virus so you should wait until the person cold sore is gone before kissing them.