From Bulbapedia, the community-driven Pokémon encyclopedia.
After trekking it out through the frozen snows of the north, you will come across an Absol in the middle of nowhere. The Absol will prance away and you will come across a save point as the two of you continue on.
After you finish storing items and saving, you head north and have the choice of either Frosty Forest or Snow Path. Snow Path is another 4 Floor dungeon that is just a side path to level up and gather some items if you did none of this before your quick departure from town.
The Frosty Forest consists of 9 floors.
Frosty Grotto consists of 5 floors with Articuno waiting on the 5th.
Articuno cannot be recruited until after the end credits
As with the other two legendary birds, Articuno has Agility, so be wary of the double speed when moving around the battlefield. Articuno also has Mist, which protects it from stat decrease, making moves such as Growl or Leer pointless. Powder Snow is the most threatening move Articuno has, as it can hit anyone in the room, no matter where they are; this more than anything will most likely lead to the consumption of Reviver Seeds if Articuno is not defeated quickly. Gust is a weaker variant of Wing Attack, but still be wary of it if you or your partner is a Grass-type or lower leveled.
After defeating Articuno, the Absol from before will join your team.
After defeating Articuno, you arrive at the foot of the next dungeon.
There is another save point where you can save and access storage. There will be no boss fight in this dungeon.
Mt. Freeze has a total of 15 floors. Snow will be falling from floors 9-15.
Mt. Freeze Peak
After completing Mt. Freeze there will be a save point and you can go to Mt. Freeze Peak.
The Ninetales you have been searching for will be waiting for you on the 5th floor of Mt. Freeze Peak. Before you find Ninetales, Team A.C.T. catch up to you. Your two teams will faceoff (you will not control this fight). While your two teams crash Ninetales will appear and explain that you are not the Pokémon from the legend. You then find out that the recent earthquakes have awoken Groudon. Team A.C.T. will go off and try to stop Groudon while you go back to town and prove your innocence.
After you do a few optional missions a Wobbuffet and Wynaut will tell you that they have put a message up on the Bulletin Board. This will be a mission for you to go to Uproar Forest and defeat a gang of Mankey.
This is the first dungeon where Monster Houses appear. Monster houses are rooms where lots of wild Pokémon fall from the ceiling of the dungeon. The rooms usually have a lot of items inside, so can sometimes be quite easy to distinguish before entering.
(Mankey can not be recruited until after the first completion of the dungeon).