Asfaloth Glorfindel's horse had saddle, the riding 'elven fashion' without a saddle is probably more like well...a fashion which takes account of the natural ways of Elves with animals...which reminds me of the letter of Tolkien regarding that.... One can also interpret this as the Noldor, High Elves used saddles, other groups of Elves may not (maybe it also comes from the relative manner of the 'sophisitication' of the culture...the more wilder more in tune with nature Nandor maybe wouldn't use these or it's a matter of choice and cultural views) the Elves the Noldor of the First Age also used saddles (Curufin captures Luthien and keeps her on his saddle: "“Then Celegorm turned his horse, and spurned it upon Beren, purposing to ride him down; but Curufin swerving stooped and lifted Lúthien to his saddle, for he was a strong and cunning horseman. "). “‘I did not know you rode bare-back, Gandalf,’ he said. ‘You haven’t a saddle or a bridle!’ ‘I do not ride elf-fashion, except on Shadowfax,’ said Gandalf. ‘But Shadowfax will have no harness. […].’” Lotr ... “At need an Eldarin rider could remain in the saddle for long hours with brief halts and light provision” The Nature of Middle-earth Tolkien writes about those matters: "I could, I suppose, answer: 'a trick-cyclist can ride a bicycle with handle-bars!' But actually bridle was casually and carelessly used for what I suppose should have been called a headstall. Or rather, since bit was added long ago (Chapter 1-12 was written very early) I had not considered the natural ways of elves with animals. Glorfindel's horse would have an ornamental headstall, carrying a plume, and with the straps studded with jewels and small bells; but Glor. would certainly not use a bit. I will change bridle and bit to headstall."
Asfaloth Glorfindel's horse had saddle, the riding 'elven fashion' without a saddle is probably more like well...a fashion which takes account of the natural ways of Elves with animals...which reminds me of the letter of Tolkien regarding that....
One can also interpret this as the Noldor, High Elves used saddles, other groups of Elves may not (maybe it also comes from the relative manner of the 'sophisitication' of the culture...the more wilder more in tune with nature Nandor maybe wouldn't use these or it's a matter of choice and cultural views) the Elves the Noldor of the First Age also used saddles (Curufin captures Luthien and keeps her on his saddle:
"“Then Celegorm turned his horse, and spurned it upon Beren, purposing to ride him down; but Curufin swerving stooped and lifted Lúthien to his saddle, for he was a strong and cunning horseman. ").
“‘I did not know you rode bare-back, Gandalf,’ he said. ‘You haven’t a saddle or a bridle!’ ‘I do not ride elf-fashion, except on Shadowfax,’ said Gandalf. ‘But Shadowfax will have no harness. […].’” Lotr
...
“At need an Eldarin rider could remain in the saddle for long hours with brief halts and light provision” The Nature of Middle-earth
Tolkien writes about those matters:
"I could, I suppose, answer: 'a trick-cyclist can ride a bicycle with handle-bars!' But actually bridle was casually and carelessly used for what I suppose should have been called a headstall. Or rather, since bit was added long ago (Chapter 1-12 was written very early) I had not considered the natural ways of elves with animals. Glorfindel's horse would have an ornamental headstall, carrying a plume, and with the straps studded with jewels and small bells; but Glor. would certainly not use a bit. I will change bridle and bit to headstall."