There are very few instances in Tolkien of anyone taking their clothes off. Like the Oxford scholars Tolkien surrounded himself with, we get the impression the peoples of Middle-earth were pretty much stapled into their clothes (actually, this is possible: sewing children into their clothes for the winter is a genuine historical practice!). Even when Frodo, Sam, and Pippin have their baths at Crickhollow, they seem to be fully dressed (though they do, admittedly, 'run naked over the grass' after being captured by the Barrow-Wight).
But there is an exception - a huge one. In the tale of Turin, his sister Nienor is driven mad by the dragon Glaurung, and flees into the woods. Her clothes get shredded along the way, and when Turin eventually finds her, she is entirely nude. This is so unusual in Tolkien's writings - I might go so far as to say unprecedented - that there must be a reason for it. Indeed, I think I know what it is:
Tolkien wanted his 'English mythology' to become the subject of classical artwork - and as we all know, 'classical artwork' is just an excuse for artists to paint naked women ('It's not pornography - it's mythology!'). So Tolkien added his very own naked woman, hoping to get the attention he desired.
It worked. Of the twenty-two images of Nienor on that page at the time of writing, seven show her with either no clothes, or seriously ripped clothes. That's almost a third. Professor Tolkien: you succeeded.