Nepal with Children

Trekking with children in Himalaya is possible? There's a recurrent misjudgement about it saying children are very sensitive to high altitude, at least in our case that's not true: they loved it! No problems up to about 4000m. We extensively trekked and climbed in the Himalaya before having children for pleasure and professional reasons, now we know next time we'll have to spend a few months in high altitude our children will happily come too...