It's almost the same as packing for yourself.
When you pack light, you can't bring the whole wardrobe so look for clothes that are light, hide the dirt, are relatively wrinkle free and dry quickly.
Like yourself, dress in layers. Be prepared to start in cool morning weather, shed a layer or two for a nice afternoon, then add layers and a rain shell if the weather turns cold or wet.
The one difference is small children can almost always get away with shorts and sandals, where an adult might look out of place.
Keeping your child's load small (one carry on in a size they can handle) will allow them to lug their own clothes. They won't mind (as long as it doesn't weigh more than they do) and you will have a lot less to keep track of. Our 12 year old was happy with a regular roll aboard. Our 8 yr old traveled a month happily with her largish daypack. Our 3 yr old grandson had a huge grin as he wheeled his little Spiderman roll aboard suitcase around the airport just like mommy.