I would suggest that you use downhill skis, the XC ones may be too slender to glide over all the ruts, etc on the lake surface. I made my fishing sled out of a old wheelbarrow ( a large plastic tub) and used old downhills, they work great.
I was going to do the same thing for my shelter, but then I saw a "Clamshell" shelter, and I think that would work the best of all. Everything right there and it all folds in in about 30 seconds, what a concept!
Anyway good luck with your project.