PoB: https://pastebin.com/Ws5M455M
Here's an idea for a league starter that I've been thinking about for a while. It converts the cold damage hit from Cold Snap into fire to ignite enemies while still dealing cold DoT and chilling, using increased cold and elemental damage and generic DoT multi to scale both DoTs.
Normally I just flesh out a tree when theory crafting, but Mathil released a Wave of Conviction ignite starter build and I decided to plug my tree and skill into his gear, just changing the some of the fire modifiers to cold (which I imagine should be cheaper this league anyway) and swapping out a ring with a Pyre. The result was higher life from the tree, fewer skill points used, and higher DPS, so I decided to share the build. It has over a million DoT DPS (though to be fair to Mathil, with Convergence checked his Wave of Conviction has 900k). That's with 5 empty jewel sockets to be filled (compared to Mathil's 0).
The cons: no Glancing Blows (though you can get it with 3 points), no exposure from your main skill (though exposure on hit is a new implicit), a little less armor, and the ceiling is definitely lower than ignite with base physical spells.
However, the chilling ground from Cold Snap should not be underestimated as a defensive layer. It's also easier to cast from a distance than Wave of Conviction, and it also provides Frenzy or Power Charges while mapping. Vortex is a comparable main or supplemental skill, sacrificing range for a shorter cooldown; in traditional cold DoT fashion, you can always use both. I would recommend using an influenced helmet crafted with Essence of Horror for a support skill like Flame Wall, Flame Surge, Vortex, etc. I'd probably also favor a staff with Whirling Barrier over a shield.
Let me know what you think!