Nords did not deal with Frost Magic all the time.
Would they not have? If Skyrim's history was similar to how its present form is in the game, it would seem that they would have had a lot of exposure to frost magic.
If they were immune to the cold they would not use fires to keep warm in Skyrim
They may prefer to stay warm compared to being cold. I am "immune" to 50 degree F temperature, but I would MUCH prefer it to be in the 70's. Temperature alone may not harm Nords, it could be associated effects that come with the cold. For example, if a Nord got stuck in an avalanche, he could die from the initial impact, suffocation, or starvation... not necessarily by freezing to death.
One problem with the game is when you have frost spells that launch giant ice shards/spears at a target. Even Nords should die by getting skewered by those... just as they would if those shards were made of anything else. In that case, resisting it simply because it's "frost" doesn't make sense to me.
You wanting the Nords to have complete immunity to frost ruins most people wanting to do Cryomage builds as well.
Hey, every choice should come with consequences, haha! Cryomages would certainly be a challenge, but Skyrim would be a very fitting place for that. Going unarmored is vulnerable to melee. Melee is vulnerable to ranged enemies. There is a weakness no matter what, only by varying degrees. Cryomages would be vulnerable to Nords, but players should know that going into the game. It's like trying to fight a dragon using only melee... if it continues to fly, you're out of luck. Switch to an alternative method of attack or simply run away. There are always options

Besides, using a mod that gives Nords such an advantage is completely voluntary. Because of that, I wouldn't suggest it to anyone wanting Cryomages to have an easy time. The main problem will simply be making the AI to avoid using frost against Nords.