The Variags wore helmets, but these are never described in detail. They may have been similar to Haradrim-, Easterling-, Orc- or even Black Númenórean designs.
MERP:
In MERP the Variags wear Helms resembling Mongol or Mongolian-Persian types as well as a fantasy form inspired by a historical Bascinet (with applied Bat-Wings).
The Lord of the Rings SBG:
In the Lord of the Rings SBG the Variags wear Helmets inspired by Mongol and Samurai helmets. Suladân is also shown wearing a Variag masked Helm resembling a Persian or Kipchaq masked helm.
LotRO:
Variag in LOTRO
In Lotro, the Variags are depicted as a mix of Varangian, Slavic and Parthian or Sasanid Warriors wearing Helmets similar to Vendel-helm designs.
Speculations[]
Similarities between Variag Helmets and the broad rimmed Orc helmet imply a possible orcish or Mordorian influence on the Khandish models.