Police in Dresden said the friends from Afghanistan were sledging in the snowy Ore Mountains in Altenberg on Sunday when the stranger approached.
“A young man approached them on the slope, wearing a steel helmet emblazoned with a swastika,” a spokesperson said.
“The stranger purposefully walked up to two men from Afghanistan (aged 21 and 26) and insulted them.
“Shortly afterwards, he hit the younger man in the head using his helmet, causing him to fall to the ground.”
The attacker continued to torment the pair until a passer-by intervened, at which point he left, but not before performing a Nazi salute.
German authorities are treating the incident, which left the 21-year-old asylum seeker needing medical treatment, as aggravated assault.
The perpetrator is also wanted for the “use of symbols of unconstitutional organisations”, which is used to ban the Hitler salute along with the display of swastikas and other Nazi symbols.
In an appeal for information, police described the suspect as aged between 25 to 30, about 175 cm tall, 5ft 10ins tall and of “muscular build”.
He was bald with facial hair resembling a “Hitler moustache” and wearing a light blue jeans and a khaki jacket.
January has seen a spate of angry anti-refugee protests and revenge attacks across Germany since the attacks in Cologne on New Year’s Eve.
Police said asylum seekers were among up to 1,000 drunken men mostly of “Arab of North African origin” responsible for sexually assaulting and robbing hundreds of women.
Opinion polls show support for taking in current levels of migrants has declined, while Angela Merkel has already vowed to make it easier to deport foreign criminals.
Around 1.1 million asylum seekers arrived in Germany in 2015, mainly from Syria, Iraq and Afghanistan.
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