Leo never wore a winter jacket. It wasn't necessary. He had an unusually warm body temperature because of his fire powers.
On the coldest days, Leo would go around Camp, to give the campers all a big hug to warm them up. It gave him the best feeling in the world, to know that he had a purpose, no matter how small.
Sometimes, Harley would cling to Leo, and refuse to let go. The other demigods couldn't help but smile as Leo struggled to carry his eight year old brother around Camp.