New main objective: Use the "Clear Skies" Shout to open the path
Press TAB and choose Magic. Head to Shouts and activate the newly unlocked Clear Skies or add it to your favourites. Head to the gate, with the thick mist behind it (screen above). At the same time make sure you don't go too deep in, as you will start losing health unnecessarily. Hold down Z to use the Clear Skies Shout, therefore dispelling the mist and unlocking the passage.
New main objective: Talk to Paarthurnax
Head forward. During your trip through The Throat of the World you will regularly come across obstacles (screen above) and each time you will need to use the Clear Skies Shout to get rid of them. Luckily it regenerates quickly, so you won't need to take brakes. However, just like with the previous climb onto the High Hrothgar, stay away from steep slopes so that you don't lose balance by accident.
The climb will also include a few battles, during which you will have to eliminate Ice Wraiths (screen above). Eliminating these monsters doesn't require magic, as you can pretty much damage them with ordinary melee and range weapons. You should consider increasing your ice resistance, raise fire damage and/or use fire spells. Don't forget to examine the piles of ice left by the demons, as they usually contain precious items.
Reaching The Throat of the World will probably take you a couple minutes, but after reaching it you luckily won't have to worry about any other threats. Instead, you will discover that Paarthurnax is a dragon himself (screen above). Before the proper conversation, Paarthurnax will decide to teach you a new Word of Power.