I thought I'd share how things went after our one-week trip.
I packed 3 sets of thermals, 2 pairs of gloves, 2 pairs of ski trousers/ jackets and 3 pairs of trousers (amongst other bits and bobs).
thermals - they were sufficient, except that we had a few accidents, and it meant I did have to do some washing after all. My advice is get pure wool (brands like Polarn O. Pyret have some warm and good value thermals) or synthetic thermals as they dry much faster. The cotton (sort of leggings) that I got for my son were very thick and warm but took 2 days to dry properly!
Gloves - my little one constantly got his gloves wet as he thought it was fun putting snow inside! So the second pair came in very handy (pun intended).
ski trousers - I packed two, one which was fleece-lined and another which was lighter. The first few days were very cold and definitely helped my son feeling warm. When the sun came out, and we did have some gloriously sunny days, then the light pair of trousers were great.
Fleeces - I packed 2 and were sufficient. Try going for darker colours, so the spaghetti sauce is not as visible ;o)
Trousers - we packed a few of these, but really just needed no more than 2 pairs of jeans.
Socks - I packed lots of socks, almost a pair for each day, and still found that I needed to wash/ dry them regularly. Every time the boys got out of their winter boots/ ski shoes, they almost always got their socks wet in the process!
I would certainly say don't bet on buying children clothes when you are at the ski resort - they are either eye-wateringly expensive or not available in the required size!
Altogether it was a great week, but now I have to go back to my laundry room!