I was tinkering around with a new subclass option, since I haven't made one before.  The Frostborn is a patron that I have had in my head for a long time now, and it wants to lend its power to those who seek it.  As this is my first subclass build, I have put everything together in my notes so far.  Here is what I have thus far:

The Frostborn
Your patron is a manifestation of the cold-heartedness of the realm.  This being's determination is to rid the world of the wickedness that brought it to life.  Its cold personality will only grant part of its power to those who are willing lose their humanity in exchange for great destructive power.

Expanded Spell List
The Frostborn lets you choose from an expanded list of spells when you learn a warlock spell. The following spells are added to the warlock spell list for you.
Frostborn Expanded Spells:
1st:  Armor of Agathys, Fog Cloud
2nd:  Hold Person, Misty Step
3rd:  Gaseous Form, Sleet Storm
4th:  Elemental Bane, Ice Storm
5th:  Hold Monster, Wall of Ice

Hand of the Frozen Heart
Starting at 1st level, your patron bestows to you powers that reflect its cold personality. Your left hand becomes of a likeness of ice. You can use the Frostbite cantrip. This counts as a warlock cantrip spell for you, but it doesn't count against your number of known cantrips.

Cold to the Core
Starting at 6th level, the pernicious ice that transformed your left hand has spread to your chest, making your resilient to cold environments. Your control of the icy spells also grow more potent. You have resistance to cold damage, and when you cast a spell that deals cold damage, you can add your Charisma modifier to one cold damage roll of that spell against one of its targets.

Freezing Conduit
Beginning at 10th level, your transformation into ice is nearly complete. Your legs have taken on this frost form. You have the ability to traverse across difficult areas with ease, leaving icy foot steps in your wake.
Your patron has also granted your more power to transform the area around you, quickly changing the tide of battle to your favor. As an action, you can strike the ground, creating a burst of cold energy rippling outward from you. Each creature you choose within 30 feet of you must succeed on a Dexterity saving throw or take 10d6 and be knocked prone. A creature that succeeds on its saving throw takes half as much damage and isn’t knocked prone. The area affected is now considered difficult terrain. Once you use this feature, you can’t do so again until you finish a short rest.

Frozen Sentinel
Starting at 14th level, you become a powerful avatar of your patron's will. Your entire body is now like ice, no longer requiring you to eat food, drink water, or even sleep, although you still require rest to reduce exhaustion and still benefit from finishing short and long rests. Your body now has the ability to reform after taking damage. As a bonus action, you can regain hit points equal your warlock level.
Your patron has also improved your ability to turn the area around you into a frozen landscape. When you use the Freezing Conduit feature, the area affected extends to 50 feet. Each creature must succeed on Dexterity saving throw or take 10d8 cold damage and become restrained until your next turn. A creature killed by this spell becomes a frozen statue until it thaws. A creature that succeeds on its saving throw takes half as much damage and is knocked prone. The area is still considered difficult terrain. You can now use this feature up to two times before needing a short rest.

I am looking for constructive feedback.  Any help would graciously appreciated.  

Looks pretty balanced. I would remove the whole body is ice thing, as some people would not like it. Maybe suggest it in the intro bit. I would also make the ba heal number of times equal to cha modifier per long rest. The freezing conduit feature is a bit op. The damage should either be reduced, or all creatures in the area make the saving throw. The difficult terrain should last for only a minute. Like the theme though!

I like it, but I agree with BramblefootDruid; maybe have the icy body flavour be described more like a range of possibilities so the player can choose if the just gain a frosty sheen, become unnaturally pale or turn to ice, keep their options open thematically.

Regarding Freezing Conduit; the damage seems pretty consistent with Cone of Cold, but being able to select who is affected is far more powerful, either it should hit everything in the area, or affect a smaller area (10 feet expanding to 15 or 20 feet at 14th level?). Also, regarding the effect, Prone feels a little strange for an action that's actively dealing damage (and can freeze a creature if killed), I wonder if it might make more sense to be a CON save or be Grappled until the next turn, as you end up frozen to the ground?

But yeah, overall I like the theme, and the rest of it seems well balanced.