Reply #4: Indeed - the idea of a salute is that the military shouldn't remove their headgear

[muriel_volestrangler]

The Coldstream Guards appear to have been the first to depart from this practice as a Regimental Order of 1745 reads: ‘The men are ordered not to pull off their hats when the when they pass an officer, or to speak to them, but only to clap up their hands to their hats and bow as they pass them’.

An extract from the Royal Scots Standing Orders of 1762 stated: ‘as nothing disfigures the hats or dirties the lace worn more than taking off the hats, the men for the future are only to raise the back of their hands to them (hats) with a brisk motion when they pass an officer’.
...
Saluting, however, should be undertaken intelligently and only when headdress is worn.

http://www.defence.gov.au/ARMY/traditions/documents/OriginsofSaluting.htm

Civilians remove their headgear; the military salute.