DES MOINES, Iowa—Bernie Sanders is struggling to gain traction with Democratic voters over age 50, so his campaign is coaching thousands of young supporters on how to talk to their parents and grandparents during the holidays.

“It’s up to us as students and young people to make the moral appeal to our older relatives to join us in voting for Bernie, because let’s face it: they won’t be around for as long to deal with the consequences of this election, but we will be,” reads a document titled “Students for Bernie: Family Persuasion...