I started skiing at 3 years old and supposedly picked it up really quick. Definitely made me love snow, I cant imagine a year without getting on snow, i might go insane! I switched to a board at 10 or so, when snowboarding really started to take off.
I would suggest starting your 3 year old on skiis for sure, but let the 6 year old decide between skiing/snowboarding. I think at 3 it would be difficult to learn how to ride a board, and strapping in, getting of the lift, etc. will make it more of a hastle. Like others have said, at that age you just want to make sure they're having fun! A good way to do this is make sure you and your husband are having fun and they'll likely tag right along. My nephew is 3 and I'll be taking him out skiing this year, so stoked!!