Ice, Fire and Half-Hot Half-Cold

Ice, Fire and Half-Hot Half-Cold are the quirks that the Todoroki family use. There may be others but in the show we only see the Todoroki family use these quirks.

 Shoto Todoroki 

Shoto Todoroki has the quirk Half-Hot Half-Cold. His left side controls fire while his right side controls ice. The ice side of him was inherited by his mother, Himura, while his fire side was inherited by his father, Endeavor. Shoto Todoroki refused to use his fire side due to that being his father's quirk and his father wasn't all that nice. He only ever used his ice because his mother never did anything bad to him, so he used his ice and only his ice.

 Toya Todoroki (Dabi) 

Toya Todoroki (Dabi) has the fire quirk. Toya Todoroki (Dabi) is only seen in Season 2 Episode 10 for a brief second and even then he is seen from behind. Later down the line he is revealed to be Dabi, one of the villains.

 Fuyumi Todoroki 

Fuyumi Todoroki's quirk is ice. Not too much is known about Fuyumi as she isn't in the show all that much

 Natsuo Todoroki 

Natsuo Todoroki is barely in the show so not to much is known about him either. He is quirkless.

 Enji Todoroki 

Enji Todoroki, A.K.A Endeavor, is the father of the Todoroki kids above. He wasn't nice to them at all until he had Shoto. He didn't care about the ohter because Shoto was his masterpiece due to the fact that he was the only Todoroki that have both his wife's and his quirks. He forced Shoto to do nothing but train. His quirk is fire.

 Rei Todoroki 

Rei Todoroki is the Todoroki kid's mother. She's only in the show for a few minutes in total. Her quirk is ice.

 Ice 

A quirk that allows the person to summon ice out of the ground. This would be useless in a mid-air fight due to the fact that it comes out of the ground.

 Fire 

A quirk that allows a person to summon fire from their body and shoot it out to a specific area. Not too effective against water quirks.

 Half-Hot Half-Cold 

A mix of the 2 quirks above. Quite powerful and not too many weaknesses to counter attack.