Have me whole, I’m a friend to your legs
Remove one letter, I’m a friend to your head
Remove once more, I become ethereal
Remove one more time, I can’t be seen but felt
Who am I?
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chair
Because:
A chair enables you to sit to give rest to your legs
Remove c -> Hair keeps your head warm
Remove h -> Air is quite ethereal
Remove a -> IR (infrared) can't be seen but can be felt.
edit: Should've reloaded to see Stiv's same answer, although a slight difference in reasoning. Quite astonishing to see similar layout.
Perhaps you are a:
CHAIR
Have me whole, I’m a friend to your legs
A CHAIR is 'a friend to your legs' in that it enables them to rest when you sit on one...
Remove one letter, I’m a friend to your head
Remove the C --> HAIR - 'a friend to your head' in that hair keeps your head warm and protects it from the sun.
Remove once more, I become ethereal
Remove the H --> AIR - one of the meanings of 'ethereal' is 'light and airy'. What can be more so than air itself?!
Remove one more time, I can’t be felt or seen
Remove the R --> AI, or Artificial Intelligence - something which 'can't be felt or seen'.
I know there's already an accepted answer, but this one also fits, to me:
Boots
because
High boots go up to your legs and protect from muck and cold
remove a letter to get
Boos, which is a brand name for cutting blocks, which in medieval times were associated with decapitation
one more letter becomes
Boo! An exclamation uttered by ghosts, traditionally, which are ethereal
And finally one last letter brings us to
BO, a frequent abbreviation for Body Odor; never felt or seen but only smelled!