Are you just talking about ice skating, or rollerskating as well?
In his autobiography, Caroll Spinney said that he did actually rollerskate as both Big Bird and Bruno. when he was on his hometowns version of Bozos Big Top, he had the opportunity to rollerskate in costume, which gave him some experience for performing Big Bird. He even mentioned rollerskating while performing Bruno (and Oscar at the same time) on a live stage.
Aslo in that same book, he said that he eventually learned to be a good dancer after Richard Hunt suggested that he make Big Bird beleive that he is a good dancer, and this actually helped.
as for ice skating in Christmas Eve On Sesame Street, i think the credits mentioend tht there were skaters from Holidays On Ice, so I guess proffessional skaters were wearing the suits. If you watch that scene, you might notice that Big Bird looks a bit thinner than in the rest of the special. I guess a lighter suit was built.
Speaking of scenes where a full-body Miss Piggy outfit is used, in a recent thread about Follow That Bird, it is said that costume versiosn of Ernie and bert were used when they were flyign the plane in wide shots.