I know that the no horses in genshin thing is probably because they aren't implemented (yet) but a lore explanation could be that they're not that common in teyvat. Mondstadt however does have them, the expedition just took the ones that weren't too young, too old or having foals while the rest stayed in a pasture in an area we haven't seen yet and now that the expedition is back the horses that went are there too enjoying a well earned retirement/vacation.
If horses ever get implemented imagine getting a tutorial quest where you come to Mond only to be like "where the hell is everybody" and end up being pointed to the pasture because it's apparently foaling season and everyone dropped literally everything in favor of baby horse.
Razor has never seen a horse before and is in awe. Jean was supposed to log the number of foals and information about them but for once completely abandoned her work because "Barbara come look at his one, it's blaze is a little heart". Fischl has declared a horse her "Black Unicorn of the Night" (it's not even true black, just dark bay). Eula is jokingly swearing vengeance on a yearling that tried to eat her cape. Varka is sitting under a tree holding a whole draft foal like a baby, completely trapped because he rocked it to sleep and can't get up until it's done napping. Kaeya and Diluc the resident horse whisperers are actually getting along shockingly well while surrounded by half the herd. Venti is singing to the foals while Albedo draws the scene. Klee is sitting on a pony, getting her first riding lesson.
You also get invited to riding lessons and given a horse because the ones left behind because they were too young are finally old enough for work and that's how the tutorial happens.