Art is so much and hard to define. I would argue that the Vikings were very artistic. Look at their wood carvings on boats especially. There are some very fine details you can see this very day on the well preserved Oseberg Ship for example.

The Vikings worked with material they had plenty off. Therefor is there no marble statues you find south in Europe for example. What they did, beside carving tree, was decorating stones and stone walls. Not only did they carve illustrations on stones (Hunnestad Monument in Sweden), they wrote heathen poems and songs on them. An example is Røksteinen (Rök Runestone) in Sweden. This stone is actually the first piece of Sweden litterateur and tells stories from Norse mythology.

You ask for music. And there was music. They made songs at feasts, after battles, before battles and when heroic people passed away or were killed in battle. Our problem is that they did not write lyrics (as we know of) and neither did they know about notes. What we do know is what instruments that were used because we have found them preserved in burial grounds and such. Mostly instruments you blow in to make sound, flutes like pan flutes and blokkfløyte, lur/lure/lurr, (a long blowing horn), wooden lyre (Greek string instruments) and horns of different sorts.

Sources: http://www.viking.no/ a very good source for information about the Vikings available in English, Norwegian and some articles are in Danish.

Norwegian: http://www.viking.no/s/life/music/n-music-iceland.html (Viking music with focus on Icelandic music)

Danish: http://www.viking.no/s/life/music/instrumenter/index.html http://www.viking.no/s/life/music/d-musikk-mogens.html