Initially, I barely had any spells and terrible equipment, so I was forced to carry a ton of potions and resort to hit and run attacks to take down enemies. I focused on enchanting, destruction, and conjuration. Switching between spells was also a pain, since the hotkey system recognized only eight shortcuts at once.
Having finished the College of Winterhold questline, I am finding it much easier to play as a pure mage, out of the robes and the mask you get in the end. My magicka regenerates so quickly that I can continually cast firebolts and flame atronachs without delay.
To conclude, if you are playing as a mage, you are only as good as the spells you know and the equipment you use. This is a big adjustment from playing as a lightly-armored warrior/archer in my previous playthrough.