I don't know if it's just me but I started playing the game over 3 months ago and not once could I find an exotic weapon all the ones I have came from season boxes and weekly missions I spent a whole week trying to find one exotic weapon and i couldn't find anything simply the game doesn't drop me exotic items.
Try to raise the world difficulty and research, which enemies have the highest possibility to drop specific exotics. Then target them precisely and at the highest difficulty you can beat them. As example: for the Bighorn, I do District Union Arena on Legendary during Invasion active there. Also some exotics need specific tasks done, like the Nemesis or Dodge City.