In the story, Hemingway does not tell us directly what we should think about the old man. He does, however, hint indirectly that the old man will die if he chooses to stay in the area.
The narrator tells us it is his job to "cross the bridge, explore the bridgehead beyond and find out to what point the enemy had advanced." From his words, we can deduce the narrator is a soldier or army scout who has been sent out to determine the direction of the enemy's advance. When the narrator notices the old man, he questions him.
The old man says he was the last to leave his hometown of San Carlos. In the rush of leaving, he was ordered to leave behind the animals under his care. The old man admits he worries about the safety of the cat, two goats, and the four pairs of pigeons he had to leave behind. The narrator, a little distracted, assures him the animals will probably come through fine. He strongly advises the old man to move on if he can.
Meanwhile, the old man tries to stand up but finds he cannot quite keep his balance. At this stage, we get the impression that the old man is too worn out to travel any further. We recognize the inevitability of his death, as he mutters to himself about taking care of his animals. The last paragraph indirectly reinforces our immediate verdict and intuition about the old man's possible fate:
There was nothing to do about him. It was Easter Sunday and the Fascists were advancing toward the Ebro. It was a gray overcast day with a low ceiling so their planes were not up. That and the fact that cats know how to look after themselves was all the good luck that old man would ever have.