As has been mentioned already by Molly, the Smith family is a group of people all bearing the last name of Smith. Therefore, "The Smiths wish you a Merry Christmas" is correct. Let's look at it another way:
"From Our House to Yours..... The Smiths wish you a Merry Christmas!"
Down the street a neighbor says to another neighbor, "what do you think about the Smiths' Christmas decorations this year?"
The response: "The Smith family always has such great holiday decorations everywhere around their house!"
If we're talking about just one member of the Smith family, say John, that's when things change a bit. "John Smith's house is beautifully decorated this year, isn't it?"
"Yes, but Mary Smith's car needs a good washing!" "The younger Smiths' toys are littering the lawn, too, not a good look."