Did the Vikings use horses in battle?

Maybe, depending on your definition of "Viking".

There was a group of Nors*m*n who traveled south into Europe and eventually came into the employ of the Byzantine Empire as elite mercenaries, eventually coming to become the personal bodyguard of the Byzantine Emperor, the Varangian Guard. The Byzantine Empire was also known for its employment of cataphracts, heavy cavalry who rode armored horses.

Whether any of the Varangian Guard fought as cataphracts is something I'm unsure of, however. At the very least, if you're including different factions of Vikings as different deck types (similar to L5R's Clans or MtG's colors), you could potentially include the Varangian Guard and Byzantines as one possible faction that would include heavy cavalry.

Additionally, the Normans under the leadership of William the Conquerer used knights during the Battle of Hastings; you can see them depicted on the Bayeaux Tapestry. Whether or not you'd count them as "vikings" when they'd settled down in France and assimilated into the local culture could be debatable, however.

Short Answer

Generally, there is no evidence in medieval sources for the widespread use of cavalry or hors*m*n in battle by the Vikings. The Vikings in Western Europe (from the late 8th century to the late 11th century) generally fought on foot. However, there are a small number of recorded cases on the continent (Francia, northern Germany) and in Ireland where cavalry or hors*m*n were either possibly or probably used in battle.

The use of hors*m*n and cavalry in battle by the Vikings over the centuries can probably be best described as sporadic at most. Also, aside from in or near Denmark, it was mostly unsuccessful.

Horses did, though, become important in raiding and probably minor skirmishes; they were obtained, sometimes in large numbers, either by trading or as part of a peace settlement or by the aforementioned raids. There is also evidence of the Vikings shipping horses to England.

Details

If we adopt the more common (and broader) definition of 'Vikings' to mean

those people from the area covered by the modern Nordic countries of Denmark, Iceland, Norway, and Sweden in the historical period c. 800–c. 1100

Source: K. Holman, ‘Historical Dictionary of the Vikings’ (2003)

then we have one possible example in an area of northern Germany originally inhabited by Saxons:

The final conquest of Saxony in 804 [by Charlemagne] inevitably attracted Danish interest. The Saxon population of an area beyond the Elbe was removed into Frankia, and the vacated lands given to the Abrodrites. 'At this point', say the Royal Annals, 'Godfred king of the Danes came with a fleet and with all the cavalry of his kingdom to Schleswig on the Danish-Saxon border.’ ….Godfred's Danes then attacked the Abodrites and forced them to pay tribute.

Source: J. Nelson, ‘The Frankish Empire’. In P. Sawyer (ed), ‘The Oxford Illustrated History of the Vikings’ (1997)

However, our problem here lies in the interpretation of the manuscript. Eric Petersen, in 'Nors*m*n in the Viking Age', has a different view: he interprets the phrase 'and the whole equitatus of his kingdom' to mean "'chiefs with horses' rather than 'horse brigade', or cavalry'.

Where the Danes got their horses from is uncertain, but cavalry may have been used again by Harold Bluetooth (died 985 or 986) when fighting the Germans:

To what extent taller horses for mounted combat were introduced in Scandinavia from the Continent is yet uncertain. Importation is however most likely especially in the second half of the tenth century, when King Harald (certainly with cavalry) fights back against German troops in southern Jutland. An earlier importation of taller horses already in the ninth century cannot be ruled out completely.

Source: Stefan Brink, Neil Price, 'The Viking World' (2008)

Medieval sources in Francia also suggest the use of hors*m*n in battle on at least two occasions in the 880s. In both these battles (Saucourt in 881 and Montfaucon in 888), Viking losses were reportedly heavy, though the numbers are no doubt exaggerated by the author, Abbo Cernuus. On Saucourt, Petersen (citing Abbo) notes that the loss of 9,000 mounted men did not deter the Vikings from quickly acquiring more horses. Later,

On 24 June 888, Odo [king of West Frankia] engaged the Northmen at Montfaucon with a small army and Abbo relates that he killed 10,000 hors*m*n and 9,000 footsoldiers.

Source: L. A. Morden, 'How Much Material Damage did the Northmen actually do to 9th Century Europe?' (PhD thesis, 2007)

Despite these apparently heavy defeats, horses were still seen as highly desirable for swift raiding, though there do not appear to be any further mentions of the use of horses in battle. Perhaps the Vikings had learnt their lesson, that it was 'rash' for

recently mounted sailors to take on Franks trained from boyhood in combat on horseback

Source: Petersen

Another (rare) example of Vikings fighting on horseback (an elite force) comes from Ireland:

Despite the fact that they fought mostly on foot, the Vikings also occasionally fielded cavalry, as at the Battle of Sulcoit in Ireland in 968.

Source: René Chartrand, Keith Durham, Mark Harrison, Ian Heath, 'The Vikings Voyagers Of Discovery And Plunder'

The ships used in early sea voyages made transporting horses impossible in practice, and raids were carried out on foot. Later, the Anglo-Saxon Chronicle notes that Vikings brought horses across to England on several occasions. They also obtained locally large numbers of horses for raiding. In 866

The Chronicle’s account of the East Angles making peace with these unwanted arrivals says that the Vikings took up winter quarters there, adding significantly that, ‘they were supplied with horses’. Asser, basing his account on West Saxon sources, adds: ‘almost the whole army was supplied with horses’.

Source: M. Whittock, H. Whittock, 'Viking Blitzkreig 789-1098'

In summary, there is no doubt that horses became an important part of the Vikings' military capability but, for them, horses were primarily a means of swift transport and sudden raiding rather than to be used as an effective cavalry force.