Story:
The story of Oath Under Snow is vastly different from other F/kl parts in both tone and style. This is an origin story of Miyu, and the story is shown from the perspective of Emiya Shirou from her world. It is a darker story in tone compared to the other F/kl entries, and it looks and feels a lot similar to the style of Fate/Zero and Fate/stay night.
Art:
The biggest problem with this movie is how the quality of animation decreases rapidly from the beginning of the second half. Considering this a movie, the fight sequences are some of the worst among all the Fate anime. Some moments look more dated than the 2006's Fate/stay night series done by Studio Deen. It's a shame since this story deserved at least a ufotable level of animation. As an adaptation from manga, some scenes were rushed, and the breathtaking action moments felt toned down. However, if you haven't read the manga, this movie will feel really interesting and the ending will leave you satisfied.
Sound:
The sound quality is amazing, I have to give it to the film. It's almost a given fact that any Fate anime will have fantastic background musics, and as everyone knows, any version of the track "EMIYA" is a beast! The sound effects are also done pretty good.
Character:
Since this is a story from a parallel world to those of Fate/Zero and Fate/stay night, it is quite interesting to see some of our known characters from those stories portrayed in a different scenario. For all the people who have been complaining how the character Emiya Shirou is "irritating" or "generic shounen protagonist", this movie has the chance to shut them down. The Emiya Shirou in this story is the best version out of all the depiction we have come across, and the steps he takes will improve the viewers' points of view about him. Miyu's characterization is also well done. As for every other characters, they didn't have much time onscreen, and as I've mentioned before, unless you have prior knowledge about them, their reasoning for their actions won't appeal much to you.
Enjoyment:
Now, this adaptation is not as good as its source material, and sudden decrease in the quality of animation might turn down your mood. Even considering that, the movie actually has good enjoyment values. There are some moments which will hit you emotionally. These moments combined with good background musics saved this movie for me, and took it up to a level of satisfaction.
So, if you are a Fate or Type-Moon fan, you will have good time watching it. If you are not one of the Fate fans yet love enjoying good anime, this can be worth your time only after you watch some other Fate stories before.
