This is a shorter way of writing でもいい, which in this construction means something like “it’s fine even if”. Together with the rest of the sentence I’d translate it as something like “so, it’s fine if it’s my victory?”.
It comes from すぎる, which is something you can add to the stem of a verb to add a meaning of “too much” to it. For example 食べる = to eat → 食べすぎる = to eat too much. In this case it’s attached to the base of 甘く見る, so it’d mean something like “you underestimate me too much”.
I think it’s just 冷たい, which means cold, but cut off halfway. I’d probably just translate it as “brr” or any other exclamation you can make when you jump into cold water on a hot day ![]()