Kristen Mills (2014) did an excellent overview of men weeping in the literature of the Viking age and concludes that it was generally frowned upon, but allowed (if not celebrated) within certain parameters.

This is based on examining a wide range of genres- in the Icelandic sagas (which deal with the settling of Iceland during the pagan era, but were written down post-Christianisation), weeping is rarely mentioned and only by women; the same goes for the Eddas that deal with mythological events. She finds only three examples of men weeping in the Eddas-

"Atlakviða, when Gunnarr and Hogni set out for Atli’s court, their followers weep, and the men of Atli’s court weep under their cloaks when Guðrún announces that she has slain her sons by Atli as revenge for her brothers’ deaths. The Atlamál poet recounts that while Gunnarr plays his harp in the snakepit, the men who could hear the music sobbed."

(Mills, p477)

Most famously, Baldr's death can be reversed if every thing in the cosmos weeps for him; the giantess Þokk cries "dry tears" and so Hel refuses to return Baldr to life. Having said that, the idea of widespread crying due to grief is clearly unusual and presented as such.

On the other hand, Mills also finds men crying in Fagrskinna, a kings saga from Norway, which has King Magnús’s death and burial, and "over his grave wept many a worthy man". The death of King Hakon sees "the king’s retainers, hearts heavy, hardly could keep from weeping".

John Lindow (2002) points to Njal's saga, in which Gunnarr af Hlarendi is falsely accused of weeping over a wound he received in battle, as evidence that weeping was unmanly- although Mills complicates this by pointing out that it is the reason for crying- a physical wound- that seems to be condemned.

So crying due to grief, particularly for a much-loved king or friend- acceptable, if not celebrated. Any other reason- unacceptable.

(Mills puts this Viking mourning into the wider European context in her PhD dissertation (available here: https://tspace.library.utoronto.ca/bitstream/1807/68979/1/Mills_Kristen_M_201306_PhD_thesis.pdf).)

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Sources:  Mills, Kristen, (2014) “Grief, Gender, and Genre: Male Weeping in Snorri’s Account of Baldr’s Death, Kings’ Sagas, and Gesta Danorum”. *Journal of English and Germanic philology,*113, pp 472- 496.

Lindow, J. (2002). The Tears of the Gods: A Note on the Death of Baldr in Scandinavian Mythology. The Journal of English and Germanic Philology, 101(2), 155-169.