Around 20-25 minutes. Take fatigue into account
This exactly, only bred racehorses can manage any sort of speed over long distance, thats carrying a lightly adapated saddle, a light as hell jockey and absolutely no equipment. These horses would be totally unsuitable for cross country riding, let alone riding significant distances when chasing someone.
Random History.
1920: The first U.S. Cavalry Mounted Service Cup race averaged 60 miles/day for five days, carrying up to 245 lb. of rider and gear.
Modern Endurance Rides: The 100-mile rides are run by the same horse and rider in under 24 hours-- but there are usually 8 vet checks, where the horse is required to rest for 30 minutes, as well as pass a health check. That's 4 hours spent resting; also, the rider may get off and jog with their horse partway. These horses are also in top condition, and must pass many vet exams.
245Lbs just over 110kilos, so basically a well built man, in medium armour and weapons? I'd say so.
If they can cover 60 miles a day racing, I'd say at full pelt your horse might be capable of covering the distance of 7 miles at night in 30 minutes. Unless you expect to tire the beast out, and expect it'll die at the end of the ride, up the speed to 22/25 minutes.
-edit
just read its a party not an individual, I'd stick with 30 minutes for a batallion riding down a target, they would have to be in some sort of shape on arrival.
