If the runny discharge is clear, it's completely normal. But if the discharge becomes gooey or turns yellow or green, call her doctor – she may have an eye infection. Allergies can cause runny eyes too.
When a cold is making your child's eyes run, the best thing you can do is practice good hygiene so you don't wind up sick too. If your child's eye symptoms are from a bacterial or viral infection, the discharge from her eyes could be contagious. (Likewise, bacteria or viruses on your hands could make her sick with another infection.)
Don't wipe your little one's eyes or nose on a towel you'll use yourself. Instead, use soft tissues or a clean washcloth to wipe your toddler's eyes. And be sure to wash your hands before and after.
Learn more about the common cold.