Cold aura spell?

[Phhase]

Is there a spell that gives the caster an aura that deals cold damage/causes enemies to take cold damage on contact? I'm looking for something to supplement the goofy-ass Armor of Agathys wiz-fight-lock tank builds I've been seeing around lately. Thinking of playing it as a grappler, for instance. The goal is to take thri-kreen as a race and make myself as close to being an Ice Devil (gelugon) as goofily possible.

As a corollary: are there any weapons that can be used in a grapple/pin/other close-up situation that deal damage automatically each turn, somehow?

[Man_Over_Game]

Flame Shield. It lets you choose between hot or cold fire. It's one of my favorites to combine with Contingency.

[Phhase]

Flame Shield.
Flame shield only affect creatures that attack you though. I want something that'll affect creatures by proximity or some other way to stop my grapples from just being chilly hugs if my target chooses NOT to attack me for some reason.

[Man_Over_Game]

I guess Investiture of Ice is pretty close. Doesn't deal damage without your Action, but it does cause the area around you to become Difficult Terrain.

[Zetakya]

Investiture of Ice makes the area around you difficult terrain, among other benefits.

[Phhase]

What's that one class feature or something that allows you to swap the damage type of a spell? Also, if there's a way to deal damage in a grapple automatically every round, then I could use Elemental weapon on a natural weapon+Elemental Bane.

[Man_Over_Game]

What's that one class feature or something that allows you to swap the damage type of a spell?

You're thinking of the Lore Wizard, considered woefully OP by anyone who's ever talked about it. Although changing damage types was the least offender in that regard (could shoot you from a mile away, against your weakest DC of his choice, for hardly any cost).

[Phhase]

woefully OP

Dayum, no kidding. Any spell, 1/long rest? Holy flexibility.

[viaFAMILIAR]

Not cold related, but if you're going to grapple, take a look at cloud of daggers. Damage on entry/turn and start of turn, for an automatic 8d4slashing/round, no attack roll or save needed.

[viaFAMILIAR]

I just took a look at the barbarian's storm herald, it has elemental auras. Rage gives you advantage on strength (athletics) checks. The nice thing about restrained is the disadvantage on dexterity saves. One aura does scaling damage on a dexterity saves with a bonus action. It's in XGtE if you have it.