Penguins and Icejades may not seem like they have much in common, but they actually complement each other so well, it's as if they were made to be played together!
To quickly summarize both archetypes:
Icejades are a defensive deck that primarily focuses on stalling and floodgating. They do this through three key cards: the field spell Icejade Cenote Enion Cradle, the spell Icejade Curse, and their boss monster Icejade Kosmochlor. The archetype's searcher, Icejade Cradle, is not once per turn.
Penguins are a control deck that focuses on interruptions and banishing your opponent's resources. The key cards are The Great Emperor Penguin, Penguin Brave, and the OG Penguin Soldier.
Important cards:
1. Icejade Aegirine - This girl carries her whole archetype on her back by allowing you essentially search any Icejade card. She also has an effect where if she's targeted for an attack or an effect, she can Special Summon any Water monster from your hand or GY. Notable candidates include Glacial Beast Polar Penguin (for a targeted bounce), Adamancipator Risen - Dragite (for a free negate), The Great Emperor Penguin (to go into the main Penguin combo as I'll mention later), or Icejade Kosmochlor (if you have the field spell).
2. The Great Emperor Penguin - A better Rescue Cat but for Penguins only. Not once per turn, so he's an extremely valuable resource. Searchable with Royal Penguins Garden.
Here are a few plays that I find myself doing frequently:
0. The main Penguin combo line: Summon The Great Emperor Penguin and use its effect to summon Nopenguin and Glacial Beast Polar Penguin. Synchro Summon into Penguin Brave and use its effect to summon Penguin Soldier facedown for two bounces. Nopenguin will also chainblock Penguin Brave to summon itself from the GY and turn Soldier's bounces into banishes. This is the main Penguin play, but if you have Penguin Squire in hand, activate its effect when Penguin Soldier is summoned to SS itself. Then Synchro into Adamancipator Risen - Dragite . Nopenguin will come back next turn when you activate Penguin Brave's effect, bringing the banish effect live again.
0.1 There are multiple ways to get out The Great Emperor Penguin. Royal Penguins Garden and Icejade Tremora are the easiest ways. Tremora herself can be searched by Icejade Cradle, which in turn can be searched by Aegirine. Aegirine's Quick Effect can also summon Emperor if the conditions are met.
1. Normal Summon Icejade Aegirine. If you have the field spell, search Icejade Curse if you are going first, Icejade Cradle if you are going second and use Cradle to get Icejade Kosmochlor. If you do not have the field spell, but have The Great Emperor Penguin in hand, search Cradle to get Tremora. Then do the main Penguin line from above.
1.1 The Icejade lockdown is essentially a one-sided Skill Drain. While it's rare to get all three key cards in your starting hand, Icejade Curse does not specifically require Kosmochlor. Therefore, if you are going first and have the field spell and Aegirine in hand, I recommend grabbing Curse to prevent your opponent from using monster effects on the field next turn.
2. Marincess Coral Anemone is an excellent Link-2 monster that can SS any Water monster from your GY with 1500 or less attack. I recommend Summoning her on your second turn to recur some resources. Candidates include Icejade Aegirine to continue setting up your floodgate, Glacial Beast Polar Penguin to bounce and go into Penguin Brave, or Icejade Kosmochlor.
3. Penguin Sword is an Equip spell that can only be equipped to a Penguin. Thus, it's not very recommended in a hybrid deck like this one. However, the effect of Penguin Sword is extremely powerful, so it's a fun option if you choose to run it. It's searchable with Royal Penguins Garden.
There's a lot more plays that what I've written here, so have fun!