January is the month of birth and turning a new leaf, for me it's the perfect opportunity to go out of my comfort zone and try out the games I usually wouldn't care for.
February is the happiest, brightest winter month, the time to bust out the winter sports games like SSX, Mario/Sonic Winter Olympics and maybe log in to Club Penguin. It's also Black History Month, a good opportunity to play GTA San Andreas
March is when the birds and flowers come back and is the most naive month, so I am gravitated towards games about childhood like Earthbound, Pokemon, Mega Man Battle Network, and also Kirby games.
April is the likeliest month of Easter, which is obviously when you should be playing Yoshi games, not only for the eggs but their childlike, playful artstyles like you'd see on easter decorations made by kids.
May is the official Mario Month, this series has a countless amount of great games to get immersed in, from the platformers to the party games to the racing games to the RPGs.
June is the most energetic month of them all, when you're finally finished with the work/school year and ready to go travel the world. Sonic games and summer sports games, like Wii Sports Resort, are my go-to.
July is the month most disconnected from your everyday reality, it's definitely the time for fantasy games and those games you might not have the time to play usually. July games include anything Square Enix, The Elder Scrolls, Ys, Xenoblade, Tales Of, Fire Emblem, Witcher 3.
I don't know about you, but August is the most prospective time of the year, when you wonder what kind of people you're gonna meet and how things will change after the summer break, my mind quickly goes to the future and I play games like Mega Man, Shin Megami Tensei, Fallout, Star Fox, Armoured Core and such.
September is the chillest month, it's too rainy outside to be active, but at the same time it's not dark and dreary either. Visual novels, point and click adventures and other text-based games draw me in here.
October is the reason I made this post, the season for (re)playing horror games like Castlevania, Doom, Resident Evil, Silent Hill, Ghosts n Goblins and MUCH more. It's without a doubt the most popular "x game season" for gamers, with how clear-cut it is about horror, and how many amazing games fit it. This October I've played a halloween-themed rom hack of Mario 64 ("Monstrous Manor", highly recommended), Metroid Fusion, RE1 and MediEvil.
Right now it's November, which is the saddest and most depressing month before the snow and Christmas arrives, so it's most fitting to play doleful, gloomy and heavier games such as Pikmin 1, Metroid, Persona 3, Final Fantasy Tactics or Valkyrie Profile. Additionally, it's the official Zelda month, so I'm replaying the classics as well as checking some rom hacks out.
December, the last month of the year and beginning of winter, is sombre yet beautiful. Games that sell this feeling include Celeste, Metal Gear Solid 1, Max Payne. Parasite Eve is the quintessential Christmas game.