But no point investing in a perfect coat for a short trip once/year when she lives in a much warner climate.
I’m going to say this all-black/all the time is a preference, not a mandate. You want to emanate confidence, not a uniform.
Can you rent a coat on the rent a dress websites??? Maybe rent a nice warm, quality fur hooded down coat (or wool or whatever) so you have the right outerwear for a southerner to feel warm but not the expense of a whole coat.
Gosh, when I mentioned coats, I was talking about myself! 
OP - I didn’t mean to suggest your daughter should purchase a coat. Sorry if it came across that way.
I just did an Instagram search for Blue Box Cafe, really none of the girls are as dressy as the OPs daughters dress. Is it just that she wants a pretty dress? It is that. My own D lived in NYC for 10 years, she loves dressing up, but winter dress up is much different than spring or summer. Whatever she decides I hope she has fun!