That said, there are several poles that would make the transition from skiing to trekking. Life-Link's Alpine Extreme Carbon Fiber Poles ($110), for instance, are made of very light carbon-fiber material, so your arms don't wear out while swinging the poles around on a downhill run. They also come with two basketsa wide one for use while snow touring, a small one for use downhilling or trekking. Or, as I do when trekking, you can take the basket off entirely. The Extremes double as avalanche probes, which may or may not be of use to you depending on whether you go Nordic skiing or snowshoeing.
Another pair that would work, I should think, are the Komperdell Titanal Trekking Poles ($85), made of a very light aluminum alloy. These are fitted with a relatively small trekking-type basket, which could work for skiing or be replaced with a wider basket if needed.
And, of course, you could always use standard ski poles for trekking, although the fact they don't collapse may be a hindrance. Check out Scott's Pro Taper Ski Poles ($89), very light and tough carbon-fiber models that could hike as easily as they ski.
Life-Link's Alpine Poles available from REI here, Komperdell's Trekking Poles here.
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