Something to do with the stupid FOM agreement.
If you player as a current driver (quick race), then you get gloves. When you play under your own name in career, then no logo gloves.
Checkout the mods section, there is probably a glove mod or two in there ....
http://www.racedepartment.com/forum/forums/f1-2012-mods.140/
Sadly the logos not showing in career mode is not something easy to fix. It is not related to textures. Its one of the xml files that states which texture files the game will load for your character model, but the file just load the "careerdriver" files, and these files don't include the logos
Yeah, it looks like there is no mod for career gloves.
In this post :- http://www.racedepartment.com/forum/threads/low-glow-gloves.60726/#post-1316145
Roberto Costa says ( I assume he is correct) :-