When you arrive at Lake Verity, you'll find Rowan holding off one of the grunts while Lucas/Dawn is up ahead facing Mars and needs your help. After going through two Double Battles you will face off against Mars who wishes to get back at you for screwing up her previous mission at the Valley Windworks.
Her team is about the same as Saturn's team, but with the difference of Purugly instead of Toxicroak. Since your Fighting-type diversity has greatly improved since last time it shouldn't have been hard to have found a Fighting-type to use against her to defeat Purugly. Be careful since it is fast and can put you asleep with Hypnosis. After the battle, despite fretting about losing again, Mars is satisfied with having captured Mesprit. She also deduces that Saturn's operation of catching Azelf it made it easier to catch Mesprit due to it sensing that Azelf is in danger and made the cave appear to head out. Mars then leaves with the warning of the power they are about to possess.
After Professor Rowan is up to speed on what happened at Lake Valor, he decides to send you to Lake Acuity in the far north where Barry is, believing that Barry may be in danger due to Team Galactic going there. It is time to head to Route 211 which is east of Eterna City or west of Celestic Town.
Route 211 contains the entrance to Mt. Coronet's north area. If you wish, you can visit the west side of this route earlier in the game when you first get to Eterna City. Travel through Celestic Town if you want to go to the east side.
Previously you could only go a limited distance into Mt. Coronet regardless of which entrance you entered on Route 211. Now with Strength, you can fully explore this side of Mt. Coronet. Besides Strength, you'll also need Rock Smash (and possibly want Defog or Surf) for traveling through. Since you won't be able to change your team until you reach Snowpoint City, make sure that your team is well prepared to handle the trainers on Route 216 and Route 217. From the entrance that leads to Route 211's east side, head north using Strength to move the boulder, and don't forget to smash the rocks to find a Rare Candy. Also don't forget to use your Dowsing Machine on your Pokétch to find some hidden items while exploring this side of Mt. Coronet. Anyway, if you follow the path downwards you'll be in B1F.
In B1F, you will need to use Defog to remove the fog and make it easier to fight wild Pokémon in here. You will find a very large pool of water. If you fish in four random squares you will find a Feebas here. Any rod will do, and Feebas is very easy to catch if you use a Net Ball or a Dusk Ball. It would also be a good idea to fish 2-3 times in each spot before moving again since it is not guaranteed you'll find one right away even if it is the right spot. Feebas' location is also changed around daily. You can also find some items here with the help of both Strength and Rock Smash. Anyway follow the western area north to find the exit to the other part of the 1F that leads to Route 216.
One new change here in Platinum is the entrance to the Iceberg Ruins. With a eventRegigigas in your party it will become a shrine to Regice. If not, it is a regular chamber that holds the NeverMeltIce. Once you have gotten the National Pokédex and have the event Regigigas with you, then you can challenge Regice to battle and have a chance to catch it. Anyway when ready head out through the west exit to reach Route 216.
Route 216 is the first area of the game to where you can catch your own Ice-type Pokémon. While Diamond and Pearl only had two you could find in the wild, Platinum has four in the regional Pokédex, though you won't find Swinub until the next route. Just remember like walking through the mud, you can't use your bike (and sometimes not your Running Shoes) in the snow. Also the areas where you walk will determine how fast you can move. Hail will be in effect in all snow areas and will damage all non-Ice type Pokémon, though Magic Guard, which Clefairy can use, is one of the few options to avoid weather damage. The lone cabin in this route will have a bed for you to rest so it can serve as a place to fully heal your Pokémon team.
Route 217 will be difficult to navigate due to both the slow movement and heavy blizzard besides having to deal with Hail conditions in battle. Also there are ninja themed trainers hiding in the snow so look for mounds in the snow to find and face them. Use your Dowsing Machine to find hidden items while you are at it. When you arrive you'll encounter the Gym Leader Maylene who is traveling to Snowpoint City not properly dressed as a form of exercise. Out of all the items you can find as you are exploring the route make sure to go to the first house in the middle of the route to find HM08 (Rock Climb). You will still need the next Badge to use it outside of battle.
If you enter the house after collecting the HM, the person inside who owned the HM lets you keep it and also gives you the Icicle Plate. Right by the house in the northeastern section of the Route is the Icy Rock where if you level up Eevee around it, it will evolve into a Glaceon.