Burning cold skill build: Three Dragons or Avatar of Fire?

If you want to burn stuff with a cold skill, there are two ways to go:

Option 1: Use Cold to Fire, and convert the rest with Avatar of Fire.
+ Fire passives boost initial hit and burning
+ Only one monster resist to worry about
- Can't shock anything or use Elemental Equilibrium
- Cold to Fire takes up a support slot
- Need to reach Avatar of Fire on the passive tree

Option 2: Wear a Three Dragons helm. Now cold damage burns things.
+ Fire skills can be used to shock enemies (major damage increase for DOT builds, as it boosts both the initial hit and the DOT, I believe)
+ Fire passives boost burning damage, but also help your fire hits
+ Potential to use Elemental Equilibrium to great effect (target is hit by cold damage, making them vulnerable to fire, and then they burn)
- Fire passives do not boost initial hit damage
- Need to manage monster fire and cold resists (burning is still fire damage over time)
- Tied to a specific helm

So which is better? My guess is that Option 1 is easier to use, but Option 2 reaches higher burn damage in theory if you make the effort to set up a huge burn with shock and EE.

Also, are there any cold skills that justify this kind of build? Ice Spear is a natural choice for its high crit chance, but the base damage is terrible.

Using option 2, you won't be able to get shock stacks without gimping your burning damage if you use EE. It takes fire damage to shock using that helm so EE will make the monsters resist the burning you were trying to get.