Islam teaches its followers to be soft-hearted with the Allah’s creatures. Feeding, curing and taking care of animals entitle the Muslim not only to be rewarded but also to be forgiven for his sins. The Prophet (peace and blessings be upon him) told us about a prostitute who was granted forgiveness because she give water to a thirsty dog. On the other hand, he told us about another woman who was deemed to enter the Hellfire because of a cat. She imprisoned her and neither fed her nor set her free to eat the rodents of the earth.
If the owner took care of the cat with regard to feeding her, but he did not allow her into his house, and that she was strong and healthy during that period. Then, he found her dead without knowing the cause of her death.
Accordingly, if he knew that she had no other place to stay in during the snowfall and he refused to allow her in, then he abandonment of her was likely a cause for her death. But if he knew that she had another place to take shelter in, then he is not blamable.