Photo by Brocken Inaglory
I don't think the nature of this beast was specified anywhere, but I can now reveal that the answer is to be found in the Eddic poem Atlamál. This is the wordier, more prosaic, and later, version of the much-told story of how the heroes Gunnar and Högni are deceived and killed by Atli, the husband of their sister Guðrún, who then takes a particularly violent revenge. Before Gunnar and Högni depart on their fateful visit, the latter's wife Kostbera has a prophetic dream of a bear breaking into their home, smashing it up and even apparently eating a few people. Her husband, like all Old Norse heroes, cannot allow such a clear warning to put him off, so he claims the dream just has a meteorological meaning (st. 18 in Eddukvæði 2014, ed. Vésteinn Ólason and Jónas Kristjánsson):
Veðr mun þar vaxa, / verða ótt snemma, / hvítabjörn hugðir, / þar mun hregg austan.
It means that a storm will grow, it will soon be daybreak, if you think of a polar bear, it means a blizzard from the east.Interestingly, this reference to a polar bear is what scholars have used to justify the manuscript title of the poem Atlamál in grœnlenzku 'The Greenlandic Poem about Atli'. There is however little real evidence for a Greenlandic origin for the poem, which the latest editors think is quite likely to be Icelandic and no earlier than the twelfth century. The story is ostensibly set in Denmark, but whether the author was Greenlandic or Icelandic, we don't need, I think, to take either their dream interpretations or their ideas of Danish weather too seriously. And we can enjoy the author's little joke in making Kostbera (the second element of whose name means 'she-bear'), dream of a bear.