In short all the skills that add things not specific to your character stats, such as arrows, javelins, party size, extra companions don't work. Just the add HP and add DMG, add speed seem to work.
Skills that add experience seem not to be working. I had all my companions in party gain the leadership 25 skills. so they increase exp to all units. I did not notice any real difference. I could be wrong.
perks that mutate the stats of weapons are also quite unsure. For example halving shields weight or damaging shields more effectively or aiming faster. I'm assuming these don't work either when you look at the horse archer perk, it doesn't allow for long bow stats to be mutated so they can be used on horseback.
Also your companions don't train their skills if not assigned to a role. A governor does not train stewardship or a caravan leader does not train roguery (outside of ransoming prisoners) and scouting and trading. An caravanleader can only learn scouting if you assign him to scout role. He will never improve trading and will never improve scouting if not assigned to the role.