There are a couple of instances where the topic of Mattie's departure is discussed in Edith Wharton's Ethan Frome. However, we first hear about it in chapter II, after Ethan picks Mattie up from the dance and her lacklustre performance in the house is hinted to her by Ethan.
We know that Mattie is one of Zeena's cousins and that her job in the Frome household is basically to serve Zeena as she tries to work in the house with her many ailments. Although many of the ailments of which Zeena complaints are probably imaginary, Mattie still tries her best to tend to Zeena and fulfill the obligation. However, now that Zeena is noticing Ethan's distinctive interest in Mattie, the talks about her performance in the house come up more often.
During the first conversation regarding Mattie's potential departure, we notice that Mattie has not much to look forward to in life, or in general. She comes from a town almost as isolated as Starkfield and it almost seems as if she is too vibrant for the type of atmosphere under which she lives. The Frome household is just about the only change that Mattie will ever see in her life, as we will come to find out at the end of the novel.
At length they sighted the group of larchesat Ethan's gate, and as they drew near it the sense that the walk was over brought back his words.
“Then you don't want to leave us, Matt?”
He had to stoop his head to catch her stifled whisper: “Where'd I go, if I did?”
The answer sent a pang through him but the tone suffused him with joy. He forgot what else he had meant to say and pressed her against him so closely that he seemed to feel her warmth in his veins.
“You ain't crying are you, Matt?”
"Of course I am not".
So there we can appreciate that Mattie is as lost as Ethan, and just as hopeless. It is no wonder that she thinks of suicide as the only way to lead a better life than the eternal winter that she lives in Starkfield.