Pretend you are going to the lumberyard as you gather up any empty cereal boxes, toilet paper tubes, boxes, etc. When you think sufficient cardboard has been provided, have your child look at the supply yard and draw a simple blue print of what he thinks he can achieve with the given cardboard. Give size limits and guidelines. You may want to take the role of homebuyer and give ideas of how many windows you'd like to see and whether it will need more than a one-story structure. Help cut windows and doors, add chimneys and porches.
Shutters are a pretty touch.
When the basic structure is complete, spread out newspaper and let the child paint the structure with white paint. If you provide a bigger house painters brush, this will go faster. One of my children used a sponge to paint her house. Dry between coats, but use up the given white tempera paint. This will give a good surface to paint the personal details.