From the Super Mario Wiki
Polar Bears appear in the The Super Mario Bros. Super Show! in the episode, Koopa Klaus. Koopa Klaus has a run-in with one after being defeated by Mario, Luigi, Princess Toadstool, and Toad in The Super Mario Bros. Super Show! episode, "Koopa Klaus." Polar Bears are also implied to inhabit the Land of Ice, as Mario warned Luigi that he might get eaten by one if he waited around instead of coming along with Princess Toadstool and himself.
Polar Bears are also enemies from Ice Climber, which also appear in the Super Smash Bros. series, where they sport shades and pink bathing suits.
The Polar Bear in Smash Run.
In Super Smash Bros. Melee's Adventure Mode, Polar Bears patrol horizontal platforms on the Icicle Mountain stage. On rare occasions, they may appear from Party Balls, but can easily be knocked off the screen with a few hits or one strong hit. In Super Smash Bros. Brawl, the Polar Bear appears once again, in the form of a stage gimmick. On the Summit, the Polar Bear will occasionally stand on the top of the stage, causing it to sink into the water. This will allow a fish to jump out of the water, and attack the players who are running in the water. In Super Smash Bros. for Nintendo 3DS, Polar Bears appear as enemies in Smash Run mode, where they attack by ground-pounding.
In WarioWare: Twisted!, the Ice Climber Polar Bears also appear alongside Topis in the microgame Ice Climber as enemies that Popo must hit with his hammer.
A cameo appearance from a Polar bear is also seen in Art Style: PiCTOBiTS as one of the pictures formed.
| Polar Bear
|| Ice Climber
| This bizarre beast appears whenever the Ice Climbers take five during their ascents. Each leap the upright bear makes causes an earthquake and makes the mountain scroll upward. If the climbers fall off the bottom of the screen, they'll drop into a bottomless chasm. For reasons unknown, it sports pink shorts and sunglasses.