If I use Froslass' "Spiteful Sigh" attack to put enough damage counters on Froslass to leave less than 40 HP on it, will its attack be prevented if Blizzard Town is in play?
No, its remaining HP is checked for Blizzard Town before you place the damage counters onto Froslass.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)
When using Froslass' "Spiteful Sigh" attack, can you put more damage counters on Froslass than it has remaining HP?
Yes, you can.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)