I've been wondering for a while now, what happens if you enchant a weapon with both fire and ice destruction spells? Do they cancel each other out or do they, as I suspect, totally ruin some villain's day?

Uhm, I'm not sure that's even possible . I'd need to check. Though I can say I'm sure one enchantment would cancel the other.

It's a good combo. They do not cancel each other out. It makes nice strong double attack. Just remember many people and creatures have good resistance to frost. Nords have 50% resistantce. Mammoths have 33% resistance. Frost Trolls, Ice Wolves, Frost Bears have resistance. Vampires are either highly resistant or immune to frost depending on level. Machines are completely immune to frost. Other than that. Frost damage is very good. Dragons. Frost Dragons have 25% resistance.

Frost enchantment has 2 second slow effect no matter what the strength of the enchantment is, so if you want to economize on soul gems, you can make a 40 damage fire and 1 damage frost.

Fire and frost are for milkdrinkers. Use shock enchantments.