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A South to North hike may be easier given your timeframe if you're worried about the cold.
I'm biased because I'm from New England but I think finishing up North is nicer. I've only hiked the parts of the AT that are in New Hampshire and Maine but Katahdin is a truly amazing place to end it whereas all the pictures I've seen of Springer seem kind of lackluster.
Also hiking through the Whites during March could be pretty rough but then again it might be similar to any winter hiking you've done in the Alps.
