As I briefly discussed in Would post-viking era Scandinavian armies and soldiers be organized and equipped any differently than other "western" medieval armies?, the Vikings certainly knew how to fight on horseback and did, but their dependence of heavy cavalry increased in course of the 12th century, after the Viking Ages.

If you wish to read a text that depicts the Viking fighting on horseback, I can cite the passage of King Harald Hardrada of Norway (d. 1066) on horseback, written by the 12th century Norwegian monk, Theodoricus Monachus:

'And as kind Haraldr himself, mounted on horseback, endevoured to draw up his battle line, his horse stumbled and he was thrown to the ground; whereupon he is reported to have said: "Seldom is a sign of this sort an omen of victory"' (Taken from: Theorodicus Monachus, The Ancient History of the Norwegian Kings, trans. David & Ian McDougall, London: Viking Society for Northern Research, 1998, p. 45 (Chap. 28)).

While longship and cargo can be used for the purpose, the most conspicuous problem of all the Vikings to bring their horse on expedition was without doubt the transportation and the food. They went primarily for raids or other activity like trading, not necessarily exclusive for the fighting.