Most adults who have the symptoms of a cold don't think twice about going to work. What they think is a cold may not actually even be a cold, but could be all kinds of other things (including allergies), because the majority of people with these irritating but mild symptoms don't go to the doctor.
If your child has what appears to be a cold, but he or she feels good, many parents conclude that there is nothing wrong with sending that child to school or to daycare. One thing you should keep in mind is that, by sending your child to school, he or she may infect classmates. Other parents might not be happy about their children catching a cold after having socialized with yours... even though colds are passed on before symptoms start showing up.
Of course, your child's well-being is the primary thing on your mind when deciding whether to keep them at home, or have them go to school or daycare. But, if you are not sure what to do in these situations, asking the school or daycare facility what their policy on such things is will be your best approach. Every parent knows that there are those days where the kid has a runny nose, but feels OK, and you just need to give that presentation at work, and can't afford to take time off. In an ideal world, colds may be a reason to keep children at home at all costs, but in the meantime, remembering that colds are good for the immune system (of the classmates your child is going to infect!) may relieve some guilt.