The same applies to children's gloves as to the ones you wear yourself: they have to fit well, offer protection, and allow your little passenger to hold on safely if necessary.
Improvising with ordinary winter gloves is undoubtedly the first thing that comes to mind, but choosing a pair of fully-fledged children's sized motorcycle gloves is a whole lot better. Impact protection, wear-resistant materials and, for certain models, waterproof properties are no luxury on the back of a motorcycle.
The outer fabric and the membranes of motorcycle clothing are more demanding than, say, a T-shirt or a pair of socks. Everything is possible, but specific maintenance products for motorcycle clothing are not a marketing trick. General detergents can damage the properties of membranes and outer fabrics, so always check the information on maintenance of motorcycle clothing.