Build:Jack of All Cantrips

Full Build Details
Get max mana at the start of the game. Do it. Don't be a wuss. This build is about being a drain on society until you unlock your wizardly potential and become absolutely fat with power. It's also a really fun way to play the game, since you need to be very mobile and careful! Not the build for you if you hate item management with a passion, sad to say.

For ice, switch the Wide White Hat with a Wide Blue Hat (or just wear the White Priest Mitre if you don't want to switch,) switch the Jade Lich Robes for the Arcane Robes, Warm with Cool, Sigil of Fire for Sigil of Ice, and Mana Ward for Mana Push, and the Explorer's Lantern with an Ice-Flame Torch. This pattern can really be repeated for any element, hell you can even do some fancy stuff with the mist boon if you utilize the Sigil of Wind + Mana Push combo, and want to whip that runic sword out.

Pro tip for dirty cheaters like me who want legacy items early: toss that Wide Black Hat into the Chersonese Legacy Chest. Start splitscreen. Make a character for Player 2. Give your Cierzo town key to Player 2. Make a new character on Player 1 with the Legacy from your OG character. Player 2 joins, grabs the legacy item from Player 1's chest. Player 1 starts their OG character & splitscreen. Player 2 drops the item. Bing bang boom, 5 minute legacy items & jewelbird masks all day, & a nifty way to duplicate items to boot.

You always have a lightning ball in Fal>Shim as long as Fal>Dez (mage light) is up, which is why you take Internalized Lexicon. Free heals and traps (especially when running ice,) are too much utility to pass up for any excursion. Lanterns are pivotal for this build, as Flamethrower switches elements based on the thing you're using. Ice Flame Torch & Explorer's Lantern will normally be your bread & butter, but you could also run with a Coil Lantern or Lantern of Souls if you want to do a Lightning or Haunted Flamethrower respectably.

Combos
Sky's the limit, kid.