I understand the dilemma! I feel it's rude to take kids out when you know they are ill. I too keep my kids home when sick..however if it's just that stubborn nose that won't quit, and they are otherwise fine, they go out. (I do keep noses clean and hands washed/sanitized to reduce germs) So, first I would ask if they are sick or just trying to shake those symptoms that persist but aren't as contagious.
Either way you decide what is comfortable for you, and if they are coming to YOUR house.....gently confronting her with your concerns, asking that they not come when ill is certainly within your right. Should your friend be offended...then it's her problem.
If you are dealing with gatherings outside your own home, then the best you can do is keep your child away from hers....or if several of you feel the same about this, kindly approach her, individually would be best so she doesn't feel ganged up on (if preserving the friendship is important) You could each say something like "Wow, ____ doesn't feel well and I bet he/she's tired. I hope my kids don't pick it up here." Maybe she would get the hint and if not, being more direct would be beneficial. Plain and simple...taking kids out when they are sick and need to be resting is rude to the other people exposed to the illness, and isn't beneficial to the child's healing. However if it's just that stubborn runny nose...then if they keep it clean and wash hands alot, extending grace so the child can get the playtime they so love would be thoughtful of you.