Thanks for the replies and for specific info on sheer drop-offs. We hadn't imagined doing the side trips, and that sounds like a good thing. There were very narrow and deep chasms in the NZ Southern Alps- a bit like miniature versions of the gorges in the Kimberley Region... You could walk almost right up to the edge without realising that you were about to step over a cliff. Fortunately on the Routeburn, being so well maintained and marked, the trail was very apparent. From all accounts, the Overland Track is very well marked?
I do appreciate people's estimates on how children of various ages might cope. It's very difficult to guage how other people's kids might hold up with different situations.
My husband has a great deal of alpine experience and winter long distance hiking in (often deep) snow in Central and Eastern Europe (Krknosse Mountains, Low Tatra's etc). I've done day walks in winter in those spots but nothing longer. My only multiday specifically alpine experience was that walk on the Routeburn Track (in September). It did rain solidly- torrentially and ceaselessly- for three days. We also had knee deep snow on the track from the about 2 km's above the Falls up to the Saddle, where we turned around and hiked back out. We had always planned to skip the actual traverse, which we knew in advance to be under deep snow and still very slippy, with a good risk of avalanche. It would have been irresponsible for us to do the traverse with the kids- it was also off season so huts were unattended with no fuel for heating. We walked two nights back out, drove around to Milford Sound and hiked in from the western end two nights to Lake Mackenzie and back out again. So we never carried more than six days of food, and I must admit our youngest didn't have a sleeping bag either, because he was in mine with me. These things would be extra challenges. But kids are generally very good with the snow and cold. We've just come back from winter over in northern/central Europe and they do quite happily manage a whole day of very physical action in the snow without problems... Far better than they cope with the heat here in Perth! It must be said that hot soup was never far away though

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I suppose in the end we must stack our own experiences against the knoweledge we have of our own children- those are our givens and the things I guess we're positioned to make a judgement on... The missing piece in the equation is knoweledge of the actual track. So thankyou for the specifics, and also for personal experiences. For example, I hadn't thought about wind as much as your experience suggests we should, Hoverbeam. I guess being largely plateau there is not much shelter if the wind picks up? Are snakes as great a risk in that neck of the woods as they are here in WA? We've encountered quite a lot of Tiger Snakes on the track whilst walking here... Are they in that part of Tasmania?
Nuts... I can well imagine the logic in having a cut off age of twelve on an escorted group hike. I know fabulous twelve year olds with whom I'd happily do many things, but walking to the corner shop would be a trial; let alone a multi-day hike!