I found private lessons for things like skiing lessons, and going slowly to build confidence, helped. My son was like that when he was younger and I was the same as a child. My dad was a firm believer in "throw them in the pool they will learn how to swim." I do not recommend this method for your child. I still have anxiety when I go skiing because my father thought I would get over my fear if he did (his version) of exposure therapy which was basically taking me to the top of a slope and telling me to get down on my own. He finally broke down and got me lessons (he was an avid skier so he thought why pay someone else to teach me what he could teach me, right? But he didn't know how to teach a terrified kid) but by that time I already had the fear ingrained and would become overwhelmed by anxiety at the idea of skiing.
Alternatively, find him a kid sitter and get out on the slopes on your own. I think he will get over it, but it may just require more maturity. He is only six, as time goes on he will get better at handling his fear of things. But I totally agree with Portia, if you don't have buy-in, and a way to get out quickly if things go south, I would not push him.
