When a question asks whether an action is right or wrong, the answer is generally going to be subjective. That means, of course, that two people who read the same story might have different answers to the same question. The best I can do is justify my position, though you are certainly free to disagree for your own reasons--and both of us can be correct.
John Oakhurst is a gambler who, along with several other "improper persons," has been evicted by the fine, upstanding citizens of a town called Poker Flats. Ironically, this town is known for its Christian citizenry, yet they sent off this band of so-called sinners with few supplies and just as winter is imminent. Three of the four, the readers discover, are as moral and self-sacrificing as any of the Christians in Poker Flat. The one true miscreant in the group is the drunkard known as Uncle Billy. The four exiles have taken shelter in an empty cabin, and soon they are joined by a young couple who have run off to be together. Tom Stimson and Piney Woods are lovely, kind, and innocent, and they spend the night in the cabin.
In the morning, Oakhurst wakes first and realizes two things: it has begun to snow and Uncle Billy is gone. The old drunkard took his first opportunity to run off with the mules and nearly all the supplies the little group had. They have enough provisions to last ten days, if they are careful, but it is snowing. In fact, it is snowing a lot. Oakhurst is unable to follow Uncle Billy's tracks, even though he could not have been gone for very long.
A week passes and the snow does not abate. Supplies are running low, and Mother Shipton dies starving herself in order for Piney to have more to eat. Finally Oakhurst is willing to send Tom down the mountain for help. Though one has already died--and eventually all of them but Tom die--I do believe that Oakhurst made the right choice in not sending Tom for help sooner.
The first evidence I use to support my position is that we know Oakhurst is concerned about the young man's welfare. We learn early in the story that Tom was gambling and got in rather above his head; when he lost to Oakhurst, the older man took Tom aside, gave him back his money, and warned him that he did not have what it takes to be a gambler. He certainly did not have to do that, but he was trying to save the boy from himself. He is doing the same thing here by not letting Tom go when he does not think he has a chance to survive the trip.
The second bit of evidence comes from this statement which Oakhurst makes before finally sending Tom for help:
"There's one chance in a hundred to save her yet," he said, pointing to Piney; "but it's there," he added, pointing toward Poker Flat. "If you can reach there in two days she's safe."
Oakhurst is a successful gambler, and he certainly understands and knows how to play the odds (as evidenced, among other things, by his own suicide once he knew he had no chance to survive this ordeal). Even after a week, the conditions were such that he knew that even a young, healthy, motivated man with snowshoes only had a one in a hundred chance to make it down the mountain alive. Imagine the odds if Oakhurst had sent him earlier.
As it is, this decision by Oakhurst saves one person from tragedy, something that is not likely to have happened if he had sent Tom down the mountain even a day earlier. It was the right choice.