Art
On Earth
Although some communities suggest that "any art by a Mando is Mando art," this sentiment is too broad to be useful as a way of defining the particular feel of "art of the Mandalorians." Rather, art of the Mandalorians incorporates at least one of a number of iconic symbols or themes. While the medium and style of such art is very different, key features make "art of the Mandalorians" immediately recognizable as such.
Stories and poems are written in Mando'a or focused on Mandalorians (but not writing that merely has Mandalorians in support roles) or aspects of the Mandalorian culture.
Visual art that is identifiable as distinctly Mandalorian has a few common elements. It prominently features at least one of the following: some variation of the beskar'ta (the chest diamond), the T-visor helmet, the kyrbes (mythosaur skull), jaig eyes, clan symbols, and any version the Mando'a script. Creating, decorating, and accessorizing beskar'gam (especially buyce, helmets) is common, both in sketches and cosplay.
Most music is either remakes of the music from the Republic Commando soundtrack, original work done in a combination of Mando'a and another language, or translations of existing work into Mando'a but set to the tune of the original piece.
This clip shows how some fans envision a marching drum for Mandalorians would look like: https://youtube.com/clip/UgkxqlyS_ykNLaPoIY8z38kfGmP4iejAnxd7?si=jqPjJmDOsxqh6pbU
In the source material
Aside from mention of Mandalorians including symbols and personalizing the paint schemes of their armor, very little is known about the style of art from Legends material.
Examples of Mandalorian visual art from Disney canon
https://www.starwarsgeekgirl.com/post-1/highlighting-some-of-sabine-s-best-artwork
https://www.starwars.com/news/5-inspirational-works-of-art-from-sabine-wren
Mandlorian artists Tojnun and other unnamed Pre-Exile Masters influenced the work of Sabine Wren: https://starwars.fandom.com/wiki/Tojnun, https://starwars.fandom.com/wiki/Pre-Exile_Masters
Sabine Wren's art work can be found in this book: https://starwars.fandom.com/wiki/Sabine_My_Rebel_Sketchbook
And here is a sample of the pages: https://www.reddit.com/r/starwarsrebels/comments/hesczq/heres_some_pages_from_sabines_journalsketchbook/
Music
Music analysis from real-world perspective: https://www.youtube.com/shorts/WrP6aEZwSAw
Jesse Harlin, Gamespot "SW RepCom Designer Diary 5" (February 14, 2005): As the final bit of polish, I created the ancient Mandalorian language specifically for Republic Commando. The Clones' ancestral language is largely inspired by a mix of Hungarian, Celtic war poetry, and Soviet proletariat work anthems.
Interview with Jesse Harlin about composing the Republic Commando soundtrack (including references to Mando'a): https://web.archive.org/web/20060615193250/http://musiconfilm.net/get_feature.php?id=6
Quote from Karen Traviss about Mando musical preferences:
https://boards.theforce.net/threads/mandoa-class-mandalorian-language.21531491/page-6#post-21556552
Mandalorian_Crusader: "Karen, would the Mandalorians have any preference in picking musical instruments or is all their music vocal?" Karen Traviss: "Overwhelmingly vocal. Occasional use of a dead thing's horn, hence the didgeridoo sound. They haven't got the space to carry round a brass band." Later, Karen Traviss added: "Don't confuse the soundtrack with what they actually have - because there's a whole orchestra in there. (There is no such thing as the Mandalore Philharmonic.) No, they don't have drums or flutes."