One pound of horse meat has about 603 calories. warhorses weigh between 800 and 2000 pounds, so the amount of calories would be anywhere between 482.400 and 1.206.000 calories. Since a grown man needs about 2500 calories a day, he can eat for another 192,6 to 482,4 days.
|Edit As has been remarked in the comments only part of the horse is edible. Apparently this could be about two-thirds of the meat in case of cows. I couldn't find any numbers for horses but since we're talking about warhorses who where not bred for eating the percentage would probably be lower. Keep in mind though that supposedly non-edible parts become very attractive as you get hungrier.|
Of course, provided he can keep the food good for so long. Since in ancient times the only place a 1000 man horse army trapped in a siege seems likely is the east, it is probably too hot for that. The only ways to keep food good in the warmer regions of the ancient world would be smoking or salting, but it's doubtful a besieged army has enough access to any of these to preserve a 1000 horses.
A horse should eat about 0,3 to 0,4 percent of it's body weight in grain, which is about 24 to 80 pounds per day, so 5 days of grain makes for 120 to 400 pounds. A male Roman citizen would eat about 4 modii of grain per month (source: my prof), making 36 liters of grain. 1 liter of (chicken*) grain weighs 690 grams, so 24,84 kilos or 54,763 pounds per month or 1,8254333 pounds per day. Thus the grain for his horse would keep him fed for 2-7 months.
I'd like to add that a desperate sally by heavy cavalry could be a much better option, and has proven succesfull in the past. An example:
"Eucratides led many wars with great courage, and, while weakened by them, was put under siege by Demetrius, king of the Indians. He made numerous sorties, and managed to vanquish 60,000 enemies with 300 soldiers, and thus liberated after four months, he put India under his rule" Justin XLI,6
*I had to weigh it myself, and i don't have any grain for horses. If anyone knows a better weight i'd be happy to recalculate (not really).