How do you get the Penguin Toss Icon?
It came from sending or receiving a gift. Riot's description in the client reads: “Acquired by having another player gift it to you during the 2015 Snowdown event.”
Is the Penguin Toss Icon still available?
No. Riot tied the Penguin Toss Icon to 2015 (gift), and it does not normally bring back past event rewards or bundles.
