He wasn't the generic "anti-social coolish cold" heroe. If you payed enough attention to his "thought bubbles", you should notice that he's scared of losing the people he loves again, that's why he kept his distance so he would never have any friends and thus safe from the feeling of losing someone importance. He only fell for Rinoa (this part is important) because she's an extrovert. You can think of Squall feeling such as one hand reaching out to his friends with the other hand cutting the bonds off (aka a war was always going in his mind). But Since Rinoa is an extrovert, she forced her into his life so that he cannot get her out and finally given up. At the end, when he finally got off his anti-social attitude he smiled. It is because even though one day he will lose his loved one, he realized that he can only feel true happiness when he open himself to everyone which is the opposite of the grumpy squall who kept his distance ("I'm gonna be ok, because i'm not alone" which is the opposite of "I'm gonna be ok, I'm gonna be strong --> stay away from everyone"). It's a very nice theme of introvert that Square put in the game, a complex theme that has never seen before in prior to FFVIII.
Edit: i forgot to mention the symbol of the white feather which will support my post better. The white feather is widely known as the symbol of cowardice/bravery in combat. Imo, this is one the best use of symbolism i have every seen in any kind of media. It's perfectly fit with Squall, a coward in the inside who always afraid facing the feeling of losing someone important and a brave warrior on the outside, who later on became the leader of the Seed.
So no, he wasn't cold, he's just scared. About one of the few 3D characters in the series (in terms of characteristics)