Unless you have a character already at lvl 80, who can buy you cold weather flying, you will not be able to fly on Northrend before level 77.
This is a long time to use grounded mounts, and it makes questing so much harder. But well – that’s how it is.
There’s only one exception to that rule. If you’re questing in Dragonblight, you can have your own flying mount, ready to use, and even for free.
Take the quest On Ruby Wings from Wyrmrest Temple. This is the fifth and final step of a chain quest that starts near Naxxramas in Dragonblight. The first quest you want to grab is called An End And A Beginning.
When you get On Ruby Wings, you’ll receive an item called Ruby Beacon of the Dragon Queen, and with this you can call your dragon to fly where you want to go.
So finish the quest, if you like, but don’t turn it in, until you’re all done in Dragonblight, or until you reach lvl 77 and can get your own permanent flying mount.