It's a question that came up tonight with a wargaming buddy of mine. I figure that since tanks were generally supposed to be supporting infantry, surely they'd carry smoke rounds along with HE so they can provide concealment as well as actual fire support while my buddy seems to think that any use of smoke by tanks was limited to the tanks defending themselves and nothing else.
Was it done at all? Was it done by one side in particular, but not by others? Were there any specific quirks to the use of smoke shells used by a particular side?
The most blatant example of the use of smoke by tanks to screen infantry is the policy of the British close support tanks which fired almost exclusively smoke rounds. See David Fletcher's brief discussion here. https://youtu.be/wOpU7ENcZvY?t=506
Smoke in US use would be certainly useful for self preservation, the US tended to prefer to blow up the enemy rather than just block their vision. However, if used in concert, instead of as simply a matter of blocking one particular line of sight in the spur of the moment, a group of tanks firing either directly or indirectly could set up a deliberate smoke screen as part of a planned attack.
Finally, it is worth noting that the 75mm smoke round on the Sherman could be used as an offensive weapon in itself: It was a white phosphorous round, which would do very nasty things to troops, and could even be used against armored vehicles. For whatever reason, WP wasn't developed for the 76 until after the war
I do not feel qualified to respond to the German or Soviet sides.