Hm... you're right, she would win.
Todoroki's weakness is that he gets affected by his own ice, he can't use ice for long because if he does he'll get too cold and get frostbite. There's his fire side though, but she can counter that using her power.
Todoroki can't alternate between ice and fire too fast either or use both at the same time, which Nora could use to her advantage because I assume she can alternate between temperatures faster than him.