I am not familiar with this expression! Maybe if there were more context to the sentence I could tell?

Perhaps a snow day, like a white Christmas? Otherwise, it would refer to the day on March 14(one month after Valentine's Day). You can google it.

The expression is not usually listed in even large-size dictionaries. I checked the British National Corpus and there is only one case of "a white day", from Ruth Rendell's 'Master of the Moor': "It had been a white day, white blank sky, white thin sun, warmish and dull". The meaning in that context seems to be "colourless" and therefore "dull" or "boring". Does that interpretation fit the context where you found your own example?

Yes, I'm confused also. "White Day" seems specifically East Asian, so if it meant that, the meaning would also need to be explained in an English essay. But then it would read, " I will arrive there on White Day!" Were there any other 'coloured days' in the essay? We don't recognise colour-coded days, apart from perhaps a red-letter day, or Black Friday. If the essay itself doesn't explain any more, then I'm sorry, it really makes little sense. :-/

maybe it's better to guess the meaning of the word from the context!!