What does an Enhance Shammy add, that a DK does not?
What are the advantages or the disadvantages?

Hex seems to be a large advantage.
Purge cannot hurt to have as an option.
Tremor, as an extra party-wide trinket vs Fear/Charm/Sleep.

A lot of the buffs are overlapping.
You could glyph Healing Stream, for Fire/Frost/Nature resist, if your healer was not a Paladin.
But Horn of Winter and Icy Talons, are the same as the Str/Agi totem and the Haste totem.

Does Enhance do as much damage as a Frost DK.
I mean once they are geared.

You lose a Death Grip, a Hungering Cold.
The single target is probably pretty good.
Do you have anything like Howling Blast at range?

Curious on your thoughts, as there has to be enough incentive for you to experiment with this.