This might depend a little on your equipment -- or your location -- but don't assume that camping is only possible in the dog days of summer. Sure, you might have to include a heavier sleeping bag (and plan around rain or snow), but luckily the house is close enough so that no one is going to be stranded in a blizzard.
Camping in other seasons presents challenges, but can be a lot of fun. In the fall, kids can be charged with collecting the prettiest autumn leaves. Or take advantage of the season and try to "camouflage" the tent with piles of fallen foliage.
Even a (not-freezing) night in winter can work surprisingly well for a family campout. If you're not sure if you can make it the whole night, compromise: build a small fire pit in the backyard, away from trees and close to an extinguisher or hose. Be sure to read up on the correct technique, but it's as easy as digging a hole and ringing it with stones. Let the kids collect some sticks and voila -- you can all gather around the campfire on even the coldest winter night.