Most of those in the nursing homes would expect you to say "Merry Christmas".
Now if you are aware that someone is of a different background (Jewish for instance) and you made a quilt specifically for that person, then referring to their holiday (in this case Hannukah) would be the gracious thing to do.
You might ask the activity director of the nursing home if there are any residents who are Jewish or whatever and consider making one special just for them.