As the scene begins, the very first thing you see is the gorgeous landscape of the Western, though it was set in Texas in 1868 it was actually filmed in Monument Valley, Arizona. Many Westerns are also shot in the same place and it's this setting which gives you that Western feel right from the get-go.
The camera follows Martha (Dorothy Jordan) out the door and pans more of the gorgeous valley scene. You can see Ethan (John Wayne) just in the distance travelling in on his horse giving the sense of a 'lone ranger' feel, a mysterious unknown man galloping in on horse with no history and no understanding of who he is really help to cement the foundations of a true Western.
The camera then shows Martha in all her glorious attire stood in front of the homesteaders house which gives Martha a background before we have even been introduced, it is clear that Martha is the lady of the household whom in her working clothes will cook, clean and tend to her husband. She also raises her hand to her head as if 'searching' for who is on their way.
Following that the camera zooms in on Ethan as he is riding in and he is set between two 'monuments', for lack of a better word, the scene behind him appears to go on for miles, and you can see the horizon which gives the idea that this mysterious man has travelled forever, with almost no beginning which links to the final scene as he also doesn't have an end.
To wrap up the scene the man of the household Aaron (Martha's husband) steps forward in an authoritative stance wearing blue jeans, a brown belt with a burgundy top and waistcoat which is a very typical homesteader outfit.
The music is key. The background track though it has that classic 1940-60 film feel more specifically it has Western aura about it, it also has a sort of romantic vibe which is possibly due to the 'obvious yet secret' love that Ethan has for Martha.
Most importantly the opening scene is key to setting the ground work for the entire film and I believe that is is just as iconic and possibly more so than the final scene.