With the weather, no money, and baby supplies limited to just what was left in the car, I really hope that she was was able to talk a family member or friend into allowing her to hideout at their home, as that seems to be the best scenario for baby Kason being safe/basic needs taken care of.
Perhaps due to her being homeless, she hasn't seen or had regular contact with some of her family/friends in a long time and could have even convinced one of them that the baby was hers?
With a baby in tow, she would be able to gain more sympathy/funds from strangers.
She hasn't dropped him off somewhere warm & safe to be quickly recovered, which would have been the best case scenario; so my hope at this point, is that she at least recognizes the value of keeping him well cared for, even if the reasoning is more about her own legal & personal benefits rather than his.