Is it safe to kiss your kids if you have a cold sore?

As a mother, any stories about weird health issues affecting children tend to catch my attention, and so it was not unusual for me to stop what I was doing to study this article from the New York Times about a three-year-old girl who apparently caught herpes in her eye after her mother had kissed her with an infected lip. So wait, if you have a cold sore, even if there is no blister or sign of infection, is it not safe to kiss your child on the face? I continued reading the article and the author, a medical student, quickly defined the answer to my panicked question.