When veterans are saluting as a flag passes in a parade (e.g. 4th of July, etc.), do we have our cover on or off?

As a veteran, we have the right to salute at parades and sporting events. It is not specified whether covered, or uncovered, probably because some branches don't salute unless they are covered (and outdoors).

https://www.military.com/flag-day/rules-for-saluting-us-flag.html

When I retired from the Army in 93 I Saluted the US Flag as it passed during the 4th of July parade. That was before all this can or can't BS came across the internet.
Neither you nor anyone can tell me when, how-to or if I can salute the flag.

The Salute
To salute, all persons come to attention. Those in uniform give the appropriate formal salute. Citizens not in uniform salute by placing their right hand over the heart and men with head cover should remove it and hold it to left shoulder, hand over the heart. Members of organizations in formation salute upon command of the person in charge.

For me I will never salute unless I'm both in uniform and covered.

When I'm on the Iowa and wearing my Iowa uniform (which is basically the Navy Dungaree uniform) I will always salute the flag when going on or off the ship, if I'm not wearing any uniform I come to attention and face the flag.

You can keep it on just as if you were in uniform with head gear on.