Good question! Since Longfellow is known to have brought elements of literary Romanticism to American poetry, and since he was a big fan of both English and German Romantic poets, we should definitely look for signs that his poems, such as "Aftermath," exhibit the qualities of that movement.
Let's explore two particular qualities of Romanticism that "Aftermath" exhibits particularly well:
1. A focus on nature.
"Aftermath" is quite literally about the changing of the seasons. The speaker conjures up images of all four seasons, mentioning snow, fields, birds, flowers, and seeds. The poem portrays nature with solemn respect and careful observation. Here are some example lines to reveal this attitude toward nature:
"When the birds are fledged and flown,
And the dry leaves strew the path;"
Here, the speaker observes how birds have grown their feathers and started to fly, and that there are not just leaves on the ground but dry ones strewn all over. This kind of minute focus on nature characterizes "Aftermath" as well as Romanticism in general.
2. A feeling of melancholy.
As you read "Aftermath," you pick up on the speaker's tone of gravity and sincerity. You can hear the serious weight of his words especially in these lines:
"With the falling of the snow,
With the cawing of the crow,"
And the poem reaches its height of melancholy as it comes to a close:
"Where the poppy drops its seeds
In the silence and the gloom."
Notice how the speaker observes snowfall and a crow's call with an almost mournful seriousness in tone and syntax, and notice how he mentions the "silence" and the "gloom" even though he's just talking about a flower dropping its seeds. The speaker seems to be sadly perceiving the changes that take place in nature, the passing of time, and of course, the sense of loss and death that come with the winter.
Take note, also, of the title. An aftermath generally happens after a tragedy: by picking that word for the title, Longfellow implies the melancholy seriousness of the changing of the seasons.
It's also worthwhile to look for an exploration of emotions in general, aside from just melancholy, when you're looking to see if a work should be categorized as Romantic. Because "Aftermath" is so short and so focused, we don't see a lot of emotional exploration besides the melancholy brought on by the changing of the seasons.