Factoring in how their personalities would factor in to this fight:
Snow will decide to take on Cloud because he's afraid of hitting girls and thinks he's the hero to take on the man with the big sword (Cloud).
Lightning would chuckle at Snow's decision and she will go after Tifa.
Cloud will nod confidentially and signal to Tifa to take on Lightning.
Cloud definitely has the upper hand against Snow. Most of the battle between Snow and Cloud would consist of Snow blocking Cloud's blows till he tires out.
However, Lightning has the edge over Tifa. Lightning can dodge most of Tifa's punches and retaliate by firing bullets.
Most likely Lightning will KO Tifa before Cloud KOs Snow b/c Snow will be on the defensive while both Lightning and Tifa are on the offensive.
The match will probably end when Lightning KO's Tifa, and Snow is staggered while Cloud is preparing to unleash Omnislash Snow. Lightning will notice Snow is going to get owned really bad, and will distract Cloud by firing a bullet at him. After Lightning has Cloud's attention, she will hold her gun against Tifa's head and threaten to shoot Tifa if Cloud does not surrender.
Cloud does not have the nerve to watch another person close to him die, and will most likely surrender to Snow and Lightning.
In sum:
Snow (defensive) fights Cloud (offensive)
Tifa (offensive) fights Lightning (offensive)
Lightning defeats Tifa
Snow is about to get killed by Cloud
Lightning threatens to shoot Tifa if Cloud doesn't surrender
Lightning outsmarts Cloud, and Cloud surrenders
Snow and Lightning win