The prologue to The Fellowship of the Ring describes the hobbits. Before the shire was settled there were three races or types or ethnic groups or subdivisions of hobbits: Harfoots, <PERSON>, and <PERSON>, that later became quite mixed in the Shire.
The harfoots were by far the most numerous and typical hobbits:
the Harfoots were browner of skin, smaller, and shorter, and they were beardless and bootless; their hand sand feet ere neat and nimble,...
The descriptions of the <PERSON> and <PERSON> do not mention if they had beards or how common facial hair might have been among them.
At the moment I do not remember reading any mention of hobbit facial hair.
I do not remember reading any mention of elves having facial hair except in the chapter "The Gray Havens" in The Return of the King Cirdan the Shipwright is described:
Very tall he was, and his beard was long, and he was gray and old, save that his eyes were keen as stars;...
<PERSON> also made an illustration in which one elf is depicted either with a beard or with dark shadow on his chin.
But <PERSON> may have forgotten about that when he answered the question of how <PERSON> recognized that Prince <PERSON> of Dol Amroth had part elf ancestry.
At last they came to the Prince <PERSON> and <PERSON> looked at him and bowed low; for he saw indeed that here was one who had elven-blood in his veins. 'Hail, lord!' he said. 'It is long since the people of Nimrodel left the woodlands of Lorien, and yet still one may see that not all sailed from Amroth's haven west over water.'
<PERSON> once wrote that <PERSON> recognized <PERSON> as part elven because no elves or part elves have beards.
So why did he write that <PERSON> had a beard?
Most of the ordinary elves mentioned in LOTR might be only 457, or 1,519, or 2,821, years old when mentioned.
<PERSON> was described in year 3021 of the Third Age. 381
The Second Age lasted for 3441 years. The First Age ended 6,472 years before <PERSON> was described as having a beard in TA 3021. <PERSON> was born 58 years before the end of the First Age, and so was 6,530 years old in TA 3021.
<PERSON> wrote annals giving <PERSON>'s birth date in Years of the Trees, but unfortunately couldn't make up his mind if the Years of the Trees in Valinor were nine point something times as long as Years of the Sun, or ten times as long, or 144 times as long as Years of the Sun.
So <PERSON> is millennia older than <PERSON>, but depending on the length of Years of the Trees, she could be 14.4 times as many millennia older.
And nobody knows the relative ages of <PERSON> and <PERSON>. <PERSON> was an important leader of elves far back in the Elder Days, ere ever <PERSON>'s father was born.
<PERSON> is probably a youngster compared to <PERSON>, no older than <PERSON>, but might possibly be as old or older than <PERSON>. <PERSON> kept changing the backstory of <PERSON> and <PERSON> (including <PERSON>'s genealogy) trying to get it right, so nobody knows.
So <PERSON> is probably the oldest elf described in <PERSON>'s works, probably by thousands of years and possibly by tens of thousands.
And so some <PERSON> scholars believe that <PERSON> as the only described elf old enough to grow a beard. 725