In one example a hero with 3 frost tokens on him battles Silence and receives a guard order attacking him again at the start of the overlord's (me) turn. My contested opinion was that each swing would require a seperate breakage roll. They player contested that the roll should only happen on the end of the players turn and happen only once at the end of the players turn and not at all on the overlords turn.
Heroes with any frost tokens remaining must role [sic] 1 power die when attacking or using a shield: On a blank, the weapon/shield shatters.
The power die is rolled "when attacking" or "using a shield." You can debate about exactly when during the attack (or shield use) it gets rolled, but it is quite clear that the roll is made during the attack action (or shield use.) This means it needs to be rolled for each attack or shield usage as long as the hero remains frosted. And yes, Guard attacks made during the OL's turn are still attacks, and the die must still be rolled.
Incidentally, the rules don't say anything about the shattering effect interrupting the attack/shield use effect. Thus, no matter when exactly the frost die is rolled, the effect that the item was used for will still be resolved. So you can debate until the cows come home about exactly when the roll is made, but it won't change how things play out.
Another question with frost
if a character gets killed with a frost token do the tokens go away or does the player still have to roll for armor and maybe shields(if used) assuming the attack did the 5+ points of damage required. This also goes with characters being one shoted by a frost attack. They die gaining a frost token
A hero who has died is returned to the town and loses half his money (round down to the nearest 25 coins). The hero’s wounds and fatigue are immediately restored to their maximum values. In addition, any lingering effects (such as burning, webs, poison, or transformation into a monkey) are immediately removed. During the next round, the hero takes his turn as normal.
Frost is a "lingering effect." That means these tokens are removed when the hero dies. A figure who is one-shotted by a frost attack is effectively immune to the frost as the tokens get discarded immediately. This is true of all lingering effects, although the Curse effect is notable in that the hero with the cursed item is required to immediately re-equip the item after being resurrected (thus regaining the curse token) or else he must discard the cursed item. The curse token does not technically remain beyond death, but it might seem like it if the hero player is unwilling to give up his item.