She gets up almost every day to find messages in her computer from people whose horses are in desperate need of help. One recent morning, a woman writing on behalf of her elderly parents who live just east of Albuquerque said, “They have scraped by every week to purchase a bale of hay for their horse, but they just can’t do it anymore.”

At $8 to $12 for a bale of roughly 60 pounds, enough to feed a riding horse for maybe three days, hay already costs five times what it did 10 years ago, Ms. Coburn said. This summer’s anemic harvest has spurred competition for a limited supply among ranchers big and small, from nearby cities and also from out of state. And as a rule, the price of hay goes up in the cold months; it doubled last winter, when the drought’s devastating effects first began to sprout.

“This winter, to be quite blunt, scares the hell out of me,” Ms. Coburn said as she walked across the corrals where the horses are kept, some of them in improvised pens enclosed not by steel barriers, but by electric fence. (The horses have arrived faster than she has been able to make room for them.)

“At this point,” she added, “it’s just too late for rain alone to solve our problems.”

Tony Pecho, the president of Illinois Horse Rescue of Will County, some 50 miles south of Chicago, has been trying to get horses adopted straight from the homes of the people who call to say they can no longer keep them. There is no money to bring them all to his farm, he said. And while calls for abandoned horses were rare in years past, this year they are the most frequent, he said, sometimes coming from places as far as four hours away.