Warning! The following contains spoilers for the Snowpiercer Season 2 episode "A Great Odyssey." Read at your own risk!
The first time Jennifer Connelly's Melanie Cavill left the train on Snowpiercer, it seemed like a death sentence for the character. It's hard to argue the vibe doesn't feel the same she's departing the train for a second time to further investigate the recent discovery that it "snowed" on Earth. Whether she's successful or not, it seems to me like the character made her biggest mistake to date.
The obvious risk is that Melanie runs into trouble on her way to the station and dies. Melanie sustained some wicked injuries on her prior venture outside of the train, though nothing that couldn't be fixed by the medical advancements created on Big Alice. This time, Melanie will have to brave the elements and stay alive for a full month before the train has a chance to come back and find her. There's a high chance of Melanie dying, obviously, which is part of the reason Mr. Wilford is so excited about it happening.
And in the hypothetical Melanie does survive, is her leaving Snowpiercer the best idea in the first place? Melanie has been shown as one of the only people to essentially checkmate the conniving Wilford to this point, so he may have a chance to cook up some schemes in her absence. Layton already has his hands full with unrest on the train. Can he really go toe-to-toe with Wilford as well? If Melanie does return to Snowpiercer, there's no telling in how the situation in the train could change in the month she's away.
As foolish as it may be, the answer for Melanie's decision is better explained in my conversation with Jennifer Connelly about Snowpiercer Season 2. Connelly spoke about her character's change between Season 1 and 2 and the natural shift in her responsibilities that come along with it.
I think she was confronted with her behavior, and I think he [Layton] was a real catalyst for change in so many ways on the train and for Melanie as a person. I think she's really taking stock of the things she's done and responsible for, and I think Season 2 becomes a period of reckoning for her. She's continuing that journey of exploring and taking responsibility for the things she did. She's in the process of getting back to the person she always was and sort of fulfilling her ultimate mission which was to be in charge of the science on the train. To help work for a successful mission.
While Melanie Cavill only just reunited with her daughter Alex and has every reason to stay and help maintain order on Snowpiercer, she also can't ignore this calling for the greater good. If there is a chance things are changing on the outside, and the world can one day return to normal, Melanie wants to do all she can to ensure humanity is ready and capable of that next step. It doesn't make her decision any less reckless, but perhaps a bit nobler.