Darkvision Class Feature with Cold Resistant Race:

Twilight Cleric 1st level (Always on, 300 feet)

The Twilight Cleric feature Eyes of Night gives Darkvision:

You can see through the deepest gloom. You have darkvision out to a range of 300 feet. In that radius, you can see in dim light as if it were bright light and in darkness as if it were dim light.

Paired with a cold resistant race (Goliath, Silver/White Dragonborn) gives the desired combination.

Way of Shadow Monk (3rd) (costs 2 ki points, lasts 8 hours)

The Way of Shadow monk can spend two ki points to cast darkvision, 8 hours no concentration. The class feature is called Shadow Arts:

Starting when you choose this tradition at 3rd level, you can use your ki to duplicate the effects of certain spells. As an action, you can spend 2 ki points to cast darkness, darkvision, pass without trace, or silence, without providing material components.

Warlock Invocation (120 feet, works on magical darkness too)

Warlocks can get permanent ability to see in full darkness starting at level 2, with the Devil's Sight invocation. (But unlike normal darkvision, it doesn't have a benefit in dim light, according to Jeremy Crawford's design intent.)

You can see normally in darkness, both magical and nonmagical, to a distance of 120 feet.

Alternatively, and not near as good for dealing with darkness, the Warlock gets an invocation at 7th level:

As an action, you gain the ability to see through solid objects to a range of 30 feet. Within that range, you have darkvision if you don’t already have it. This special sight lasts for 1 minute or until your concentration ends (as if you were concentrating on a spell). During that time, you perceive objects as ghostly, transparent images.

Once you use this invocation, you can’t use it again until you finish a short or long rest.

Gloom Stalker Ranger (3rd): Umbral Sight:

At 3rd level, you gain darkvision out to a range of 60 feet. If you already have darkvision from your race, its range increases by 30 feet.

Shadow Magic Sorcerer (1st): Eyes of the Dark:

Starting at 1st level, you have darkvision with a range of 120 feet.

Druid/Ranger/Sorcerer/Wizard/Artificer (2nd level spell darkvision, lasts 8 hours)

Any class that can cast darkvision yields the desired combination. The level that darkvision becomes available varies by class. It's not concentration, has a cast time of 1 action, and can be cast on yourself or someone else. It gives 60 ft range darkvision.

Cold Resistance Class Feature with Darkvision Race:

Storm Herald Barbarian (Tundra) 6th level

The Storm Herald Barbarian can gain cold resistance at 6th level via the Storm Soul feature.

Fathomless/Fiend/Genie Warlocks

Three different Warlock subclasses give cold resistance.

Fathomless (6th level), Oceanic Soul:

You gain resistance to cold damage.

Fiend (10th level), Fiendish Resilience:

Starting at 10th level, you can choose one damage type when you finish a short or long rest. You gain resistance to that damage type until you choose a different one with this feature. Damage from magical weapons or silver weapons ignores this resistance.

Genie (6th level), Elemental Gift:

You begin to take on characteristics of your patron’s kind. You now have resistance to a damage type determined by your patron’s kind: bludgeoning (dao), thunder (djinni), fire (efreeti), or cold (marid).

Tiefling with the Infernal Consitution feat.

This one is tiefling exclusive; tieflings have darkvision, and the Infernal Constitution feat gives the resistance:

You have resistance to cold damage and poison damage.

Eldritch Adept feat.

The Eldritch Adept feat allows you to select an invocation, and the Devil's Sight invocation mentioned previously is eligible.