This writing prompt is an incredibly difficult prompt. Naturalism is just not a currently popular genre. I believe a big part of that is due to the fact that people generally like reading things that are happy or at least end happily. Naturalism tends to be quite pessimistic and deterministic; therefore, it is often a depressing read.
Naturalism is closely related to realism, so any modern-day example of naturalism should also be influenced by realism. A key point of naturalism is then that it pushes the realism to show nature as coldly indifferent to mankind. Nature and the universe exist, and man is forced to struggle against their relentless, uncaring onslaught. Furthermore, nature is sometimes shown as a force that is simply waiting for human characters to make that one mistake that will cost them their lives.
Readers can easily see these themes in both "The Open Boat" and "To Build a Fire." The men in the boat struggle and struggle for hours on end, hoping against all hope that a break in the weather will allow them to safely get to shore. They take their final risk, and nature casually kills, with no care about how hard the men previously worked. The man in "To Build a Fire" is in a similar situation. He is able to keep nature at bay as long as he can start his fires, but nature deals him the ultimate punishment when his final fire is poorly placed.
The best modern day example that I can think of for displaying elements of naturalism is Andy Weir's book The Martian. It was made into a movie, but the movie doesn't quite convey Mars's onslaught against Mark Watney. The book was heralded as ground breaking because of how Weir wrote with intense realism, despite the genre being science fiction. Weir had Watney working with existing technologies, so that is where the realism comes into play; however, it is the fact that the entire story is about Watney's struggle to survive on an entirely hostile planet that shows readers elements of naturalism. Mars is in wait the entire time for Watney to make a critical mistake like that of the man from "To Build a Fire." Mars is definitely an antagonist in the book, but it is a difficult "bad guy" to hate, because deep down, readers know that Mars doesn't care either way about Watney, his survival efforts, and his desire to survive. That's naturalism.