Currently I am playing as a Battlemage (half swords, half magic, enchanted heavy armour) and am loving it but its raised a question mark in the inner workings of my head:

If I decided to be a full Warrior (i.e. abandon magic altogether) how would I defend myself against enemies who wield magic? Likewise if I decided to become a full Mage (i.e. only use magic and abandon armour and standard weapons and only wear enchanted cloaks) how would I defend myself against archers and melee weapon wielding enemies?

Enchantment (for the warrior), shield spells (for the mage). There will be a little mixing of classes in both cases but I think you could pull it off.

For the warrior: get some resist enchantments or potions for when you need them and overall just accept part of having more health is sometimes you have to roll with the damage. This is actually part of the reason I've always liked playing Breton warriors, natural resist magicka.

For the mage to defend against mundane damage: Alteration school spells; things like Oakflesh are life-savers.

There's a Restoration spell - Lesser Ward - Gives me +40 Armour and +40 spell-blocking (can't remember exact terms). It doesn't have a duration, though, but in some fights, it's been worth my warrior (who's a practical sort) giving up carrying a shield to constant-cast it. Drains Magicka fast, but worth it, especially since you can then switch back to shield.