From Destinypedia, the Destiny wiki
Players start out in the Headlands and need to head towards the Ember Caves, where the House of Winter's Lair can be found. Fight through or run past the Fallen guarding the entrance to the caves. Inside, where the first Darkness Zone is activated, there will be Vex and Fallen fighting each other; the distraction helps make it easier to dispatch the enemies, though there is one Hydra at the bottom of the cave that should be dispatched quickly.
Objective: Unlock the gate while defending against three waves of enemies
This outdoor area also has a large number of Vex and Fallen fighting each other. A good place to start is to walk left and take out the Hobgoblins, using the vantage point to eliminate the remaining enemies. Once all enemies are eliminated, Ghost will begin hacking open the door to the next area. This will cause three waves of Vex to appear in the middle of the area (returning to where the hobgoblins were will help avoid crossfire). The first wave is mostly Goblins and three Axis Minotaurs. The minotaurs are all close to each other, so it's very likely that they will all fire at the same time with their torch hammers, making adequate cover essential. In the second wave, three Axis Hobgoblins will spawn on the ledge, as well as several more on the ground with a few goblins mixed in. The third wave has several Harpies, as well as two Axis Hydras. The door will open after all enemies are dispatched.
Players will encounter four unoccupied Pikes; these can be used to eliminate enemies along the way, but are not necessary. The fireteam will travel along a long canyon with some Vex blocking their path, including three Minotaurs, but they can be dodged or dispatched quickly with the Pike's guns. At the end of the canyon are two Axis Hydras and some Goblins and Hobgoblins. One Hydra is on the ground but the other one is on the ledge, which is inaccessible to the Pikes. Dispatch both to make it to the final area of the strike.
Boss: Aksor, Archon Priest
The area ahead must first be cleared of all enemies, which includes a few Vex but also several Captains and a large number of Dregs armed with dual Shock Daggers. Once all enemies are dealt with, the cell containing Aksor will open. Aksor fights just like Riksis; he is a Captain armed with a Shrapnel Launcher who will teleport and smash anyone who gets near him. Therefore it's best to keep one's distance from him, he may even teleport directly in front of you and smash you, so be ready to run away quickly.
One of the best vantage points at the beginning of the fight is the ledge directly overlooking the cell, though enemies will occasionally spawn there. Reinforcements typically include Shank swarms, High Servitors, and eventually Stealth Vandals and Captains. The first wave will appear shortly after Aksor, with the Vandals and Captains appearing towards the end of the fight. The key is to take out the reinforcements quickly while maintaining awareness of Aksor's position to avoid getting surprised by his melee attack.
It starts out normally enough. Proceed as normal until you reach the Ash Coves. In the Ash Coves there will be several Taken Blights in your way, with several Taken Minotaurs and Hobgoblins with them; defeat them with your Pikes or ignore and continue your way.
Winter's Run (Taken version)
Boss: Nixis, Hunger of Oryx
When you arrive the Archon Priest's cell is replaced with a massive Taken Blight that cannot be shot at. Fallen will be fighting with Taken, so it is best to clear them out before engaging the boss himself. Approach it and Nixis, Hunger of Oryx spawns. Like his Fallen counterpart he is a boss version of a Taken Captain with all of its abilities, plus the ability to summon lesser Blights for reinforcements.
Defeating him will be tough as he is more powerful than Aksor. Unlike Askor he tends to hide in the cave portion of the map so it is recommended you have a Nightstalker to tether him where you want and suppress his abilities, particularly the Taken Captain's shadow-blast.
Taken enemies here are more numerous than their Fallen counterparts, and will need perseverance to defeat them effectively; an awareness of where the Blights are will help prevent the debuff Shadow Touched, which suppresses your abilities. If you're not careful your team can be outflanked and overwhelmed. Like Aksor, the key is to take out reinforcements while damaging Nixis as quickly as possible.