Why does Grass Wonder often have a pole arm? Is it an irl reference or just a meme?
Short answer: Grass wields a naginiata (Japanese glaive-like polearm) when her unique skill procs in game.
Long answer:
IRL Grass Wonder has one of the sweetest temperaments around for a racehorse, which Cygames "translated" into the game by making her a Yamato Nadeshiko (traditional ideal Japanese woman). The Yamato Nadeshiko archetype comes with a naginata, because women of the warrior (bushi) class were expected to defend their households when their husbands were out on war or other business. The naginata is the traditional preferred weapon for this, and often comes together with the woman's dowry.
IRL Grass Wonder was also said to have an "indomitable" warrior-like spirit, because he was able to persevere and overcome a serious leg injury and win multiple races. This ties in with his uma counterpart also being given a "warrior" motif with in-game titles and character skills referring to it, and meshes nicely with her naginata as well (which also pops up in her unique skill animation, as mentioned).
As for why Grass seems quick to anger and pull out her naginata in various fan comics... both the anime and game and various shorts canonically allude to her as being not so nice under her facade when pushed, with El Condor Pasa and occasionally Golshi drawing her (subdued yet potent) ire from time to time. The IRL Grass Wonder is also, despite being absolutely sweet and obedient around humans, not a pushover around other horses, with noted rebel-who-wouldn't-cow-to-any-authority Gold Ship immediately freezing up and paying his respects to Grass when the latter shot him a single look.
She slices, she dices, eviscerates, and decapitates, sees in the dark, and can track you by your DNA. Just like the girl whose ice cream you ate last night.