No, Elemental Crit DMG affixes are independent of the Weapon Element. You can use Fire and still have High Voltage.
If you are using an Ice MH weapon with Ascendent or Prismatic, Ice DMG %, Ice DMG + and Freeze affixes will apply to the element that they switch to. So if you have +100% Ice DMG, +5000 Ice DMG and 10% Freeze, what ever element your Ice MH switches to due to Ascendent or Prismatic will receive the same benefits. However, lets say you have an Arcane OH, even if this Arcane weapon switches to Ice, it will not get any benefits.