from Starkfield and was busy pursuing a life away from the family farm when he came home to fulfill his duty as a son to his ailing mother.  If it had been spring and Ethan could have easily travelled back to school for the following term and life would have been easier, he may have stayed only long enough to formulate his plan to leave again, but winter loomed long and he couldn't bear the thought of being alone.  Once he is married to Zeena he gives up his dreams of college and pursuning a degree.  He tries his best to eek out a meager existence on the failing farm and he patiently deals with Zeena's hypocondria.  It is only when Mattie Silver comes to live with them that there is a light in his life again, but she is a dream that can't be achieved.  Ethan can't bring himself to just leave Zeena with no means to support herself.  After the failed suicide attempt and the crippling of Mattie and Ethan there is truly no hope that anything will change.  The three of them live a quietly miserable existence in the broken down house and we see the truth of Mrs. Hale's  observation that there is very little difference between the Frome's in the house and the Frome's in the graveyard.  Ethan's not leaving in the winter of his mother's death is the seed of all the subsequent misery of these characters.

Ethan’s marriage to Zeena took place during one of Starkfield’s long, cold winters. It was also after a long period of pain and sorrow, when Ethan was growing desperate between the impending death of his mother, her silence, the overbearing coldness, and the prospects of living alone forever in the farm. All of these feelings were exacerbated by the darkness and the coldness outside. Therefore, when Zeena came to become Ethan’s mother’s caretaker during that winter, she filled every single void in Ethan’s life during that particular long and horrid period of time.

Her efficiency shamed and dazzled him. She seemed to possess by instinct all the household wisdom that his long apprenticeship had not instilled in him. 

Even though seasons do change, even in Starkfield, Ethan Frome still never gave a second thought to his future. Instead, he focused entirely on his immediate present, on his mother's death, on his fear of loneliness, and on the feeling of uneasiness that the never-ending winter made him feel. Therefore, in a moment of haste, and of fear of being alone, Ethan asks Zeena to marry him.

When he saw her preparing to go away, he was seized with an unreasoning dread of being left alone on the farm; and before he knew what he was doing he had asked her to stay there with him.

Therefore, Ethan realizes that he had made this decision in haste, and only because of the feelings that he was having at that moment, under those circumstances.

This is why he wonders if things could have been differently had these variables been also different in his life. If his mother had died in a different set of circumstances, including the weather, could things have been different for Ethan?

Another, less cordial perspective to consider

We could also analyze this from another perspective. Ethan, who is a bad decision maker, is questioning whether the weather at the time of his mother's death played a factor in one of his many flawed life choices.

While the question is obviously figurative, it is also risible, considering who is asking it. What difference could the weather have made in his decision to marry Zeena, when Ethan continuously makes flawed choices, despite of anything?  Any doubts on this statement should be put to rest when looking into Ethan’s choice of agreeing with Mattie to commit dual suicide by sledding into a tree. 

Having established that Ethan just does not think things through, it is clear that he never really analyzes his rationale behind marrying Zeena, until he starts having feelings for Mattie.

Interestingly, Zeena knows better, and even reproaches Ethan for having asked her to marry him for mere convenience. Therefore, if even Zeena can tell what a bad choice maker Ethan is (and so is she), it is clear that only Ethan would have asked himself the asinine question of whether the weather would have made a difference in making a choice to get married.

Back to the question of the weather

Regardless of whether the question of the weather makes sense or not, the reason why he asks the question in the same from both perspectives discussed. He really wonders if the factors that were in place at the time that his mother died, and when he chose to marry Zeena, could have made a difference in his life if they had been different factors. Whether the question is logical or not, does not matter. The mere fact that he is asking the question is indicative of his current state of desperation, and his desire to see his life change, for good.