[Neil Jones]

While many Christmas specials of shows aren't set at Christmas, they're still clearly made as special episodes to be shown at Christmas,

This was the case with Dad's Army, the three Christmas specials they made (1971, 1975 and 1976) you wouldn't know they were Christmas specials as they just look like normal episodes. This may be more to do with the plot of the show though, since I know in reality Christmas would be celebrated, albeit it maybe in an air raid shelter somewhere...

There are probably no end of other (Christmas special episodes of shows that don't look like Christmas specials) examples - Keeping Up Appearances comes to mind (the first Christmas special was themed, but the others weren't') and also Some Mothers Do Have 'Em - the episodes where Frank learns to drive and fly respectively.

And of course other shows pulled out all the stops and then some more to make the Christmas show a resounding success - obvious example here being The Morecambe & Wise show.