In terms of Echinacea purpurea extract, it is an herb that has been more extensively studied, than other herbal medicines. Consider that these studies have all been done in adults, so not much is known by the scientific community about the risks and benefits in children.
Echinacea has been widely used for the treatment and prevention of the common cold, and to relieve symptoms from some chronic diseases. In general, studies have found Echinacea to be relatively effective in reducing the length of cold and flu symptoms, as you have observed in your own household, but there is a long way to go before a consensus is reached on this point. It has not been found effective in preventing colds.
Most of the studies of Echinacea have shown it a to be safe herb with very limited side effects. The most commonly reported side effect when it is taken by mouth is a mild allergic reaction. Patients with certain diseases should not take Echinacea. For a list of these conditions, you should consult with your doctor.
Remember that Echinacea has not been studied in children, so side-effects specific to the pediatric population are unknown. A recent study does suggest that Echinacea and some other commonly used herbs may be harmful to cells of the reproductive system, but this effect is only seen after very high doses of the herb are present. Furthermore, it seems as if sperm cells are the target of these harmful effects, so pre-pubertal boys would not be at risk because they have not yet begun to produce sperm.
There appears to be little possibility that Echinacea causes sterility in pre-pubertal children, but because there are no human studies, we cannot say with absolute confidence that there is no risk to young children.
In summary, Echinacea is generally regarded as safe, but always consult with your child's pediatrician before beginning any type of medication.