Vile of Volatile Ice is a cool item and it would be dope if we could make Skeleton Rogues also benefit from that, making cold spec Lich have their own cold typed melee skeletons to utilize (and to die around you)
This is a minion ability, so the conversion to Ice would only work if the Acolyte had this ability. If the ability isn’t there, then the conversion won’t happen.
Your idea is good, but it’s not feasible.
The OP wants the unique to convert the Skellie Rogue’s skill as well as the (player character) Rogue’s skill… “All” they have to do is add an additional line to convert the other skill.
We already have similarly conditional item Lethal Concentration.
It would create a potential balancing complication of making rogues a cold minion skill. Though I do not think it is a problem because skeleton archers can become a cold minion skill by specialisation tree alone.