When set up to conform with certain match rules, probably at Sea Girt and similar ranges, the sticking point would be sight radius. The normal rifle used in US military-rules matches 1900-1914 was the Krag with a 30" barrel, but with a sight radius closer to 26" or 27". On the HW, the 1901 or 1902 Krag sights were mounted close to the action, placing the tiny peep closer to the eye, an optical advantage. But the Winchester barrel needed to be shorter than 30" to meet the rules.
The match results were published in Shooting and Fishing, sometimes with equipment lists. Walter Hudson was normally listed as a member of the NJ National Guard team. W.Milton Farrow was listed as a member of the DC National Guard team. If they were shooting at 600 yards or greater, they may well have used their Winchesters.