An animation featuring two chibis wearing tiger and dragon costumes duking it out
It is Etotama, an anime currently airing this season (Spring 2015).

Synopsis from MAL:


  The anime's story revolves around Nya-tan, the cat of Chinese astrology who wants to become a member of the Chinese zodiac. [...] She meets Takeru Tendo, a high school student who lives alone in Akihabara, and becomes a freeloader at his house. Little by little, she gets closer to her goal.


The anime's setting is built upon this folk story, which explains the origin of the 12 animals in the Chinese Zodiac via a story about a race between the animals to become part of the zodiac. The Cat in variations of this folk story were always tricked by the Rat in one way or another and missed its chance to become part of the zodiac.

The scene you describe is from the second half of episode 1, where Nya-tan (Cat) and Doratan (Dragon) brawled out with each other to give Nya-tan the setting of "a tragic heroine who's shocked because the Dragon Eto-musume she thought was a friend ended up being a traitor".

A screenshot from around 16:33 of episode 1, showing both the Cat and the Dragon.



A screenshot from around 17:52 of episode 1, showing the Cat being restrained by multiple icicles.