Why does Todoroki look different between the 1st and 2nd season? In season 1 of My Hero Academia, Todoroki looks like this:



In season 2, he looks like this:



As can be seen from the first image, his left side (and not his right side) is his ice side. His left eye is also round and red. I believe there is only 1 short instance in season 2 when he activates his fire power where his left eye becomes round and red.

Another difference is that in season 1, Todoroki's left side is always encased in ice, but never in season 2. Even when he uses his ice Quirk extensively in season 2, he is only seen with a little ice on himself:



What is the reason for the difference between season 1's and season 2's Todoroki?
In the first picture, it was Todoroki wearing his hero costume. In episode 6 to 8, they had mock battles wearing their costumes. It is also explained that the students can give their own design for their costume.

The second one, it's in the Sports Festival where they cannot wear hero costumes because they will have an advantage to their enemies.



Regarding freezing and shivering, if you're referring in the 1st picture, no, he won't freeze because that is just his hero costume, not his quirk at work.

But if you're talking about his quirk, then the answer is still no, because he uses the other half of his quirk which is 


   half hot


to keep himself from the effects of his half cold and vice versa.