In "The Lake House", while Kate is waiting in the restaurant, that scene is interspersed with some skating. What does all this switching back and forth between Kate waiting in the restaurant and athletes skating on ice mean?
Maybe you already know this, but just to make sure, first of all those skating scenes aren't interspersed with Kate out of nothing. They are not anyone's dream or a mere metaphor (at least not only), but happen right there in front of the restaurant and can be seen by her through the window. This is evident in the first scene that shows the skaters through the windows of the restaurant from Kate's point of view.
Now to the meaning of the skaters. I would say they were added as a classical romantic winter/christmas element to underline the romantic atmposphere of the whole situation, since ice skaters have been used as a symbol for the enjoyment and romance of winter in many movies before.
The skating field emptying over time and the skaters getting fewer and fewer is then used to emphasize the passing of time that Kate waits in vain and the tilting of the situation from romantic anticipation to sad disappointment. At the end there is only a single couple left dancing on the ice, which Kate stares at, envying them for the love they apparently share and that she thought to find herself, too (or to have found already), but which she disappointedly didn't find this evening (not yet knowing the sad reason for Alex's disappearance).
So to sum up, the skaters weren't just interspersed with the real scenes, but were observed by Kate in realtiy and served the purpose as a classical romantic winter symbol and the development of the skating field and its inhabitants underlined the emotional stages Kate went through on this evening.