Would you mind sharing the article (or at least the citation)? I'd love to see what it references.

Much of our information about Viking-Age hygiene derives from three types of sources: (1) contemporary accounts by outsiders, (2) Old Norse accounts often written centuries after the Viking Age, including many of the Icelandic sagas, or (3) conjecture.

Contemporary accounts are sometimes positive about Viking-Age Norse, and sometimes negative, but it's important to remember that they're typically hyper-local. For example, when Ibn Fadlan saw that Norse traders in Russia would pass a bowl around to wash themselves in the morning, we have no reason to assume that farmers in Iceland or the Faroes were doing the same thing.

Later Old Norse accounts have a similar problem of only describing small slices of the Viking Age, and they often flesh out authentic memories of the Viking Age by introducing 'common sense' details from the day-to-day experience of their later medieval authors. It's often hard to parse Viking Age from medieval details, particularly with regard to incidental things such as hygienic care, which wasn't exactly a hot topic for the oral historians among the Norse-speakers of the Viking Age.

Conjecture is, of course, the worst, since we have a very different set of values and experiences that guide what we think of as 'common sense'. Re-enactors and their academic counterparts—'experimental archaeologists'—produce a lot of valuable information through trial and error, but hygiene is simply not an area where trial and error can be an appropriate guide. Most people living in the modern West possess ideas about dirt and germs that would seem out of place in the Viking Age.

But even if we accept that there's a lot we can't know about day-to-day living in the Viking Age, we actually have some interesting clues that allow a partial answer to your question. In particular, wealthy women were often buried with artifacts that archaeologists call 'toiletry sets'. These could include things like tweezers, ear scoops, and scissors, often made of iron and looped onto a belt at the waist. I haven't done a close study of these artifacts, but my sense is that they're almost always found in women's graves.

This tells us a few things. It tells us that hygiene was associated with prestige, and that it was managed by women. That is, of course, similar in some ways with many contemporary societies today. Interestingly, it also suggests that hygiene wasn't so much about how you looked (e.g. are your eyebrows plucked?) but rather about having —and showing off—the right tools (ever seen an ad for the Art of Shaving? or checked out an electric toothbrush or razor left on a friend's sink?).

With these things in mind, it's doubtful that thralls would have had much access to the level of hygiene that communicated prestige. It's possible, of course, that just as Viking-Age women were responsible for managing the food and wealth of a household, they might also have been responsible for managing its hygiene. In some ways, this makes a lot of sense (effectively putting a head of the household in charge of disease control), although that doesn't mean it was necessarily so. In that case, having a slave with clean ears could communicate that an effective matron was running a household, whereas seeing a slave picking out his earwax might suggest poverty and mismanagement to any observers. That is, at least, what the archaeology suggests, taking into account both the artifacts themselves (toilet kits) and the places where we find them (rich women's graves).

And just to add another element into the mix, it's important to remember that both masters and slaves were highly mobile during the Viking Age. One of my favorite examples is an Icelander named Hoskuld, who served the Norwegian king for a time, and acquired an Irish concubine at his court. She raised a son who became Olaf the Peacock, a popular character in later sagas, and it's interesting to think about what might have shaped his hygiene practices most: the Norwegian court his father had aspired to? the Irish court that had been the birthplace of his mother? or the Icelandic farmstead where he himself was raised?

So you've posed an interesting question that really gets at the diversity of the Viking Age, and I think it's apt to sum up with the historian's (an archaeologist's) favorite answer: It depends on the context. :)