属于省略。
张道真《英语语法大全》下册第 390 页:
表示善意祝愿的句子中,I wish you 常常省略:
(I wish you) Good luck!
(I wish you) Happy birthday!
(I wish you) Good night!
(I wish you) Good health!
(I wish) A happy new year to you!
(I wish) The same to you!
祝福中每个单词首字母一般要大写(显得正式),也可以不大写,但作为专有名词的节日首字母必须大写:
Christmas, Valentine's Day, Women's Day, Children's Day...