Cryogonal can only be caught within Twist Mountain with a 1% chance outside of Winter, when this rises to 5%.
Although the odds of you encountering this elusive Pokémon is rather low, and it has the physical defense of wet tissue paper, it is a rather useful utility Pokémon due to its high Special Defense, Special Attack and competent support movepool backed up by STAB Ice Beam to plough through certain threats with relative ease.
Gym #7 - Brycen (Icirrus City, Ice-type): You can take on his Vanillish with Flash Cannon as you have a good Special Defense to tank the Mirror Shots fired back. Beartic will survive one hit and then instantly destroy you with Slash, so stay away from this and Cryogonal, the later simply due to being a mirror match of special attacking special walls, a physical fighter is better for convenience.
Bianca (Route 8): She leads with Stoutland, which will destroy you with Retaliate, don't bother. While you do wall Musharna, and Light Screen makes it even more so, it will attempt to force you out with Hypnosis but you should win out. Serperior is risky as, while you will one-shot it with Ice Beam, Leaf Blade will hurt unless you have set up Reflect prior. Engaging Emboar/Samurott is suicidal due to their impressive physical competence against the snowflake's terrible Defense. In regards to her monkey, Simisage is an easy target for an Ice Beam but the other two will be able to take a hit and then slowly wear you down with Scald/Flame Burst respectively, while you can't do much back.
Gym #8 - Iris/Drayden (Opelucid City, Dragon-type): Unleash frozen hell upon any daft enough to engage you. Just make sure that you can one-shot Haxorus and Druddigon, as failing to do so will result in death.
Cheren (Route 10): Unfezant is laughable with both Air Slash and Razor Wind bouncing off our frozen ally while it freezes the bird back. The elemental monkeys are the exact same as they were back on Route 8 against Bianca, same rules apply here. Emboar and Samurott can still crush you with little effort between Heat Crash and Aqua Tail respectively, while Serperior still is somewhat of a challenge without Reflect. Liepard actually is somewhat threatening with Night Slash, but a few Ice Beams should put it in its place; just set up Reflect on Unfezant.
Elite Four Shauntal (Pokémon League, Ghost-type): Cofagrius is not threatening due to its mostly special-based offensive moveset with Will-O-Wisp only being a minor inconvenience, spam Ice Beam. You do wall Jellicent, but nothing you have can scratch it either beyond potential Toxic stalling, just set up a Light Screen and bail out. Golurk provides a decent switch-in in Set mode if you have a Ground-weak Pokémon out at the time, but Shadow Punch will kill Cryogonal if you mispredict. Ice Beam should easily take it out in one hit, though, if you play your cards well. Chandelure has an insane Special Attack to fire off STAB super effective Fire Blast, which even Light Screen will not cover you from.
Elite Four Marshal (Pokémon League, Fighting-type): How about you reconsider why Cryogonal being anywhere near this fight is somehow a good idea? Everything will OHKO you with ease so for the sake of the Pokémon, restrain from even trying to set up screens here.
Elite Four Grimsley (Pokémon League, Dark-type): Stay away from Scrafty and Bisharp for obvious reasons, they will withstand any attack you throw at them before flattening Cryogonal with STAB Brick Break/Iron Head. Krookodile should go down to one Ice Beam, and while Liepard may do a chunk of damage with Night Slash, you should be able to take it down.
Elite Four Caitlin (Pokémon League, Psychic-type): Her entire team are bulky special attackers, set up Light Screen and then start firing Ice Beams. Just be cautious of Reuniclus' Focus Blast, Also do be aware that Gothitelle does have Calm Mind.
Reshiram/Zekrom (N's Castle): Zekrom is a no-go as Fusion bolt = dead Cryogonal. Reshiram is not that much better as while there is a decent chance that you could withstand a Fusion Flare behind Light Screen, Slash will tear through Cryogonal like a hot knife through... ice.
N (N's Castle): In regards to his dragon, see the above point for Zekrom. Reshiram might be manageable behind Light Screen, but Fusion Flare will still be doing uncomfortable amounts of damage. Vanilluxe is an easy target due to only being able to exchange Flash Cannons with you, Light Screen and your own Flash Cannons will trump it. Both Archeops and Carracosta carry Stone Edge, one's faster and the other will take a hit, so stay away; Cryogonal can take on Archeops if it has a Speed-boosting nature, though. The same applies to Klinklang, simply because you have no way to damage it, even if it has a fully special moveset. Screens are a decent option here before switching out if you lack a suitable Hidden Power. Zoroark can use Retaliate to crush you and Focus Blast and Flamethrower will leave a mark.
Ghetsis (N's Castle): Cofagrius is more annoying than Shauntal's, simply due to having Toxic and Protect to stall you, either set up Screens and spam Ice Beam or switch to something able to take it down faster. Bisharp and Bouffalant are terrible ideas due to being powerful physical fighters and Eelektross can crush you with Wild Charge. Using Seismitoad as a target to setup Light Screen is a viable option, since it will make a certain Pokémon much easier to handle. Speaking of dangerous Pokémon, Hydreigon will overwhelm you if Cryogonal is underleveled, with Fire Blast. However, Light Screen will make taking down this triple headed menace significantly easier.
Post-Game: Turn that Garchomp into an ice cube, and anything else weak to Ice will fall to your icy wrath. You can also handle Kyurem as well, just slap Flash Cannon on and get ready for a tough fight.
Cryogonal will come equipped with Mist, Haze, Aurora Beam and Acid Armor. Shortly after you obtain it, Ice Beam shows up at level 33 and instantly becomes your main method of attack from here on. Level 37 brings both Light Screen and Reflect, which are viable options due to Cryogonal's impressive Special Defense and its immunity to Ground-type attacks. Slash, at Level 41, is not worthwhile due to Cryogonal's measly Attack stat. Confuse Ray comes at level 45 and is actually quite useful against special attackers. Recover is priceless for a defensive Pokémon at level 49 and beyond that Solarbeam, Night Slash and Sheer Cold (levels 53, 57 and 61 respectively) are not ideal with the later two being postgame-only.
In regards to TMs, Cryogonal carries a decent selection of moves. Toxic is pretty useful if combined with Protect, which allows you to handle special attackers you are unable to hit normally. Hidden Power (preferably Electric, Fire or Grass) and Flash Cannon provide extra coverage in your offensive arsenal. Rain Dance is niche option as it will support any Water-types you have while negating your Fire weakness.
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
What Nature do I want? Modest is nice, as Cryogonal has no reason to use its physical movepool and the buff to Ice Beam brought on is rather useful. Timid is also decent for similar reasons, as the Speed buff helps it outspeed certain Dragon-type threats as well as Archeops.
How good is Cryogonal in a Nuzlocke? It's reasonably good, with the ability to mess with several prominent threats due to its high special stats and reliable set up of both screens. However, the threat of a strong physical move shattering it does mean you need to be careful.