Did you pack well enough for the cold? Allie gave great advice on some basic things we need while we're in Northrend, like food and other consumables. Depending on your level of progression or gear, your approach to questing or leveling out here will vary quite a bit. For well-geared players, it'll be a breeze to go through most of the zones as gear of item level 146 and beyond (Tier 6 / Season 3) will last a fair bit past Level 75 or so.
While the bare attributes on those items such as Intellect or Strength will often be superior to most quest rewards, other statistics will begin to fall behind such as Hit, Crit, or even Haste as we level and the ratings we need for those to scale become bigger. Here is where lesser geared players get a bit of a helping hand. The plate greens of Northrend, as well as the occasional blues are loaded with Hit, Haste, and other important stats. If you're going to Northrend dressed in blues or even item level 120-123 epics, you'll be able to quickly replace pieces that have scale appropriately with your level. In the end, it will all even out.
The gear you have now, as in right now, that's all you'll need to be in Northrend. There's no need to look for upgrades, no need to spend Badges of Justice or Honor, and no need to even do anything. Just go into Northrend, quest (or get BoE drops), and pick up what comes your way. To help you, here's are some recommended rewards in the starting zones for players who aren't very well geared yet.
RETRIBUTION / HASTE
Retribution Paladins looking to gear up through the starter zones should look into Howling Fjord, where there is a good assortment of Haste items. It's going to be very tempting to stack up on haste, and if you're merely picking up gear to level, then it isn't such a bad stat to pursue. If you happen to be Level 68 or a fresh Level 70, the green rewards will be excellent leveling tools for you.
1. Runeplate Helm
If you're a Horde player, this is a reward from Adding Injury to Insult, which is a mini-quest chain involving the Vrykul in Baleheim. The pre-requisites for the quest are Baleheim Must Burn! and Baleheim Body Count, which awards Scavenged Tirasian Plate. For the Alliance, the helm is a reward from Mission: Eternal Flame, which requires destroying some Plague Tanks around Halgrind.
2. Ramshorn-Inlaid Shoulders
Horde players get this at the end of a short quest chain right at Vengeance Landing. Test At Sea is a boming-type quest that leads from The New Plague, which also awards Antique Reinforced Legguards. Alliance players only get this after a relatively longer quest chain which involves riding a harpoon near Utgarde Keep. The quest It Goes to 11 is the only part of the chain that rewards gear.
3. Scavenged Tirasian Plate
As mentioned, the Horde get this rather easily from Baleheim Body Count. The Alliance, on the other hand, get this from Return to Valgarde, which is part of a longish quest chain and is the only quest from that chain with any gear rewards.
4. Onyx Grips
These melee DPS gloves are a reward from Stop The Ascension!, which is started by a random drop from the mobs in Skorn.
5. Antique Reinforced Legguards
Alliance need to complete a short quest chain for these plate legs. The quest, Anguish of Nifflevar, can actually be completed on the way to It Goes to 11. As mentioned, the Horde get this from The New Plague in Vengeance Landing.
6. Ghoul-Crushing Stompers
These boots are a reward from Bring Down Those Shields, with Alliance and Horde versions. This quest involves taking down crystals along the west coast of Howling Fjord, between the Apothecary Camp and Westguard Keep.
7. Featherweight Claymore
Horde players get this very easily from A Tailor-made Formula, just to the west of New Agamand. This is part of one of the more fun Horde quest chains in the zone. Alliance have the quest The Delicate Sound of Thunder, which is a pet-type exploration quest in the Baelgun Excavation Camp.