Vortex

Hypothermia wouldn't work.

I decided to pick up a level 3 Empower that was corrupted so it only gives me +2 levels, but that was actually a nice boost for my build and it was only a few chaos - so you're right about it being serviceable. The way I built my character the clear speed is plenty good as is the AOE size, even without the AOE radius support gem.

Vortex could use an effect skin. How about a Shaper Vortex skin? Would be pretty cool to have that skin and many may be inclined to purchase it as well

can vortex dot leech?

Assuming i'm using Elemental Equilibrium.

If i Change Pyre Ring with Hrimburn Gloves.

I would Do Less Damage with the DOT Effect because the mobs get more resistant to the DOT damage.

Can you confirm this thought?

Let's first cover your first case with using Pyre. The DoT would not be changed to Fire damage due to Pyre. So, the initial hit from Vortex, being converted to fire, would increase all affected mobs' resistances to Fire. Correspondingly, their resistances to Cold and Lightning would be decreased, allowing the cold DoT to deal more damage to those affected by the initial hit.

The important thing to remember with conversion is that damage over time effects cannot be converted from one type to another. Another important thing to remember is that none of the ticks of damage from a DoT effect count as "hits." Thus, DoTs do not trigger Elemental Equilibrium, Life Leech, or Life Gain on Hit.

Following that, let's cover your Hrimburn case. Since the initial burst of Cold damage from Vortex counts as a hit, then those affected would take reduced damage from the subsequent Cold DoT of Vortex. Now, the burn effect from Hrimburn would enjoy reduced resistances from Elemental Equilibrium, so that could possibly work to your benefit.

Tl;dr - Yes, you're right, the DoT would tick against mobs with heightened Cold Resists and deal less damage.

I want to see spell knockback in this game. With the reverse knockback from the unique gloves you could make an actual black hole sucking in enemies. That would be nice touch with the new mtx. Note this is not about usefulness, just about the theme.