"All fear the sniper and the sniper fears no one." The Axis sniper is the German equivalent of your sniper. They have the same abilities and are dangerous.
If not found and killed, they can create serious trouble in your defense lines. A close air support could be able to kill most hidden snipers, but in cases of the sniper blitz waves may not eliminate all snipers. Enemy snipers will prioritize enemies by rank rather than class, but more often than not this will be the Officer.
Snipers do not move straight down, rather they wander around looking for a view to kill from.
Concentrate fire on a cloaked sniper will work. Infantry will fire at the sniper, regardless of the fact that they can't see the sniper.
Heroism is commonly used to protect useful soldiers from being assassinated by one of these guys. The employment of Allied snipers is often recommended to counter enemy snipers and other infiltrator units.
All German snipers have blond hair.