After you kick Team Flare out of Frost Cavern and rescue the Abomasnow, Mamoswine returns to Mamoswine Road.
Explore the Road
While on Mamoswine Road, you might encounter Sneasel, Delibird, Snover, or Abomasnow.
To climb onto the Mamoswine, walk onto it from the side. While riding the Mamoswine, you can press A to smash rocks that are in your way. To hop off of Mamoswine, press B. You can't get off of Mamoswine while you're in the deep snow.
First, go east until you reach a couple of rocks. Press A to smash them out of the way, then go to the rocks to the north and smash them. Then press B to hop off of Mamoswine.
Follow the east path if you want to battle Sky Trainer Anila. She has a level 42 Rotom and a level 44 Butterfree. Remember that you can only battle Sky Trainers with pokémon that have the Flying type. Other types of pokémon can't participate in the battle.
Go back to where you parked the Mamoswine, then go west. Soon the path turns to the north. Turn on the Dowsing Machine to find a hidden Timer Ball in the dead-end to the north.
Go east from there to find an Icicle Plate. If a pokémon holds it, its Ice-type moves will be stronger. In addition, if Arceus holds it, it becomes an Ice-type pokémon, and its Judgement move becomes an Ice-type move.
Now go back to the Mamoswine and hop back on. Go back into the deep snow. Go south and look for some rocks to the south. Press A to smash them out of the way, then go south to find another rock. Press A to get rid of that one, then press B to get off of the Mamoswine.
Follow the path to the west, then at the fork in the road go left to find a Calcium.
Go back to the Mamoswine and hop on, then go into the deep snow and go east. Follow the path south, then smash the rocks to the south. Go east and press B to get off of the Mamoswine.
Keep walking east and you'll receive a Holo Clip from your neighbor, who challenges you to a battle in front of the Anistar City Gym.
Turn on your Dowsing Machine to find a hidden Paralyze Heal just north of the gatehouse to Anistar City.
Go north along the narrow path to find a Rare Candy.
Now go east to Anistar City.