I don't know about Russian units, but allied units would have them available depending on location and mission. You don't carry anything into combat unless it is needed. U.S. troops would probably carry them at the squad, platoon, or company level. One reference, that I cannot verify or remember which period, mentioned that a typical combat load included three frags and a smoke grenade. The trouble is that if a soldier carried everything they 'might' need, they could not move. For example, it was often the case that they would lose gas masks, often just keeping the case to store other supplies in. In a basic infantry configuration, each soldier had to carry clothing, food, water, his weapon, hundreds of rounds of rifle ammunition, and usually ammo for any crew served weapons attached. And some parts of the squad/platoon would also have to struggle under the weight of things like radios, flame throwers, etc. When I was radio man in a squad, we often had spare barries carried by some of the troops.

If you were in areas with no armor, air, or artillery support, smoke would often be useless. Thick jungle can render grenades limited in their usefullness. If smoke cannot penetrate the canopy of trees, even with air support, smoke would not help the mission.

__________________
Lord, let me be the person my dog thinks I am.