I was looking the official site from Nexon and saw a post of a experiment they did about what skills you can use while mounted, regarding our archer class I will translate the results:
Archer: You can use all the skills while mounted except Kneeling shot
Ranger: Can use all the skills.
Quarrel shooter: Deploy pavise X
Stone Picking X
Teardown X
Hunter: Can’t use any hunter skill while mounted
Sapper: Can’t use any sapper skill mounted
Wugushi: Throw Gu Pot X
Jincan Gu X
Scout: Camouflage X
cloaking X
Distortion X
Rogue: You can use only Sneak hit
Fletcher: all skills available
Falconer: Can’t use any skill
Cannoneer: Cannon Shot O
Shootdown O
Siege Burst X
Cannon Blast X
Musketeer: you can use only Headshot while mounted.
Source> http://tos.nexon.com/community/gos/view.aspx?n4ArticleSN=32