Flydog's answer is the most logical: Greatest number of troops could see the event, if done at dawn.
Those shot at dawn would have been deserters. This kind of crime was especially odious, because it was a crime against not just the state - but to all their fellows in the army. Loyal soldiers would be very hateful of deserters, knowing some of their comrades had died just because others refused to do their jobs.
(eg, Typical army conversation after someone deserted:
'What happened to Larry?' 'Got hit by a shell, on the squad's left flank.' 'How could that happen? Wasn't Tom supposed to be on guard there?' 'No, Tom deserted. Probably off having some beers with his buddies.' 'So that's why Larry had to die?
So that Tom could have some beers with his buddies? Boy,
just gimme five minutes in a dark room with Tom, and....
well, you get the idea.)
Criminal justice once especially involved participation by the whole community, believing certain crimes were 'sins' against the whole community - Army desertion especially so, thus it had to be done as the most-public-event possible, at dawn.