I just started studying Blender and my goal is to create a 3D game.My question is simple, everything that is textures of fur or hair in the characters is first done in Blender (or a similar program) or in a videogame engine like Unity?
Sorry for the bad inglish
Well both, but it depends on how complex the hair is. Something like this: https://cgcookie.com/course/creating-hair-cards-for-realtime-characters was done in Blender and it uses fancy textures and modeling to make realistic looking hair. It's static, but it looks good. If you want something realistic that moves around like real hair you're looking at complex shaders like this: https://www.youtube.com/watch?v=p1JZijEO3B8 that uses compute shaders and mimics hair physics. Hair and fur in general in games can be quite expensive for games that's why they tend to have lower poly hair that doesn't move around much. At best they might rig the hair to look more realistic.
It's awesome that you've started studying Blender with the goal of creating a 3D game! To answer your question, fur or hair textures on characters are usually first created in Blender (or a similar program) using particle systems or texture maps. Once done, they are then imported into a game engine like Unity for further refinement and integration into the game. Blender is fantastic for modeling and texturing, while Unity handles the game’s interaction and physics. By the way, if you're looking for inspiration, you might want to check out this link to pin up for some cool design ideas. Keep pushing forward!