So I think that most people, especially in Skyrim, would consider frost magic more death magic than fire, because necromancers are known to use it. However on the other hand fire could also represent death magic, first lets take a look at both.
Fire
The reason fire would be associated with death spawns from hell. Hell is generally depicted ablaze, the "fires of hell". Many demons also have flaming eyes or breathe fire as well. Evil spirits become fiery when enraged, thus the death aspect.
Frost
The main reason frost is considered death magic is the necromancers of course. However when you think about it, bodies are cold after they die. Ahzidal's ring of necromancy makes the undead explode to frost not fire, also the draugr use frost magic.
The Theme
Personally, I think it depends on the theme of the build/character which would be death magic. A grim reaper focused on skulking in the shadows while his undead fight for him, would probably be backing them up with frost. But a flaming warrior of death clad in daedric armor would prefer to roast their foes to prepare them for hell.
What do you guys think is more Death-esque?
I would have to give this round to Frost. Though fire certainly gets connected to death in some works, notably those involving Hell, it seems far too "lively" to be associated with death for me. Frost, on the other hand, seems much more "dead". It is unmoving and cold, whereas fire is really very active. I don't think your "Flaming Warrior of Death" embodies death as much as he does evil, which fire does a nice job of portraying. The difference comes down to the fact that Frost is a very depressing substance.
Honest,y Shock is better. The magic strikes faster and fewer enemies have defense against that element and in Skyrim it drains magicka, which makes it potent against mage-types.. If I had to choose between Fire or frost, I'd go Fire for several reasons. It also flies faster than Frost, can be used for survival (fire/light/heat/cooking/etc), and often comes with additional damage over time whereas Frost tends to just slow an enemy.
That's a tough one.
In one aspect, death is cold, much like a corpse is cold; while fire is the warmth of life.
In another aspect, cold numbs and puts to sleep, while fire causes searing pain and agony.
So I guess it really depends on what aspect of death you're going for. If you're shooting for a corpse / sleep aspect, I would say Frost. If you're going for the pain/agony/burning in a lake of hellfire, go fire.
So it would be the actual Drain health ability? Sir you have necromancer and Blood mage confused, Blood mages use life force to heal themselves and to KILL others(Drain health) while necromwncers use illusions and fear based abilities- Now I am going to say this, Dorian, one of the companions for DAI, was a Necro but the skills that the auto level up gave him Fire based abilities! I guess Fire is a Fear based thing, as for feeling goes, definitely go for frost. It all depends on the skill set of the Necromancer who is being controlled by you. So you choose, should you use the Illusion perk Aspect of terror for fire? Or will you be like every other necromancer?