Ethan Frome is not a Gothic novel in the classic tradition of Poe, for instance, who almost always uses the elements of the supernatural, fear, darkness, ghosts, horror, death, decay, madness, secrets, double characters, castles, etc. in his poetry and fiction. Wharton herself explains the Gothic influence that permeates Ethan Frome and her other short novel Summer as being rooted in the tradition of Nathaniel Hawthorne. It has more to do with the bleakness of the landscape and its influence on the characters.
Think about Ethan's wife Zeena and his relationship with her. Both are decidedly psychologically tortured, which can be considered gothic ( idea of the imprisoned soul). They can not break away from each other. This is repeatedly emphasized through the bleakness of the New England surroundings.
Finally, some scholars argue that Wharton wrote in the tradition of American female ghost-story writers like Mary Wilkins- Freeman i.e. ( Wharton herself wrote ghost stories as well).
If you have access to databases through your library try Project Muse or MLA, there is quite a bit of research on this that is easily accessible. I have attached a link to an article that is generally available online or through your library.