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?