It just seems like, if you're attacking a well-fortified position with little to no cover, you'd want to conceal your movements at least long enough to get off the landing barge.
Smoke screens were used during Operation Overlord, primarily to obscure the Allied ships and landing craft of the invasion armada from German artillery, and to obscure the landing forces from aerial attack, as well as to obscure the British ports from which the invasion was launched. Air units such as 342 Sqn RAF were responsible for "[laying smoke screens] over the invasion craft."
However, their tactical use was somewhat limited by the harsh weather conditions of the day. Edward Samuel Farrow states in Gas Warfare that effective smoke screens had several significant requirements, including that "it may be assumed that the width of the screen should be from two to three times the width of the object to be concealed" and "in a wind of over 20 miles an hour it is very difficult to form an opaque smokescreen" (Farrow, 97). Wind speeds on Omaha Beach, where fighting was fiercest, averaged 12-18 knots (~14-21mph) on June 6 (Bates, 19).
Despite these issues, "Final plans for the use of large area smoke screens during the cross-Channel attack provided for smoke over the ports of England from which the invasion would be mounted and smoke over OMAHA and UTAH beaches in Normandy. In both cases the screens would be used as a means of concealing activity from German aircraft" (Birdsell and Kleber, 355).
These smoke screens would be the responsibility of "Chemical decontamination troops, scheduled to go ashore with the initial landings, [who] were at first to use smoke pots and M2 generators to provide any necessary smoke" (Birdsell and Kleber, 356). These authors note the difficulty of landing the "heavy" M1 smoke generator on the beaches, while the troops only had access to 48 of the lighter M2 smoke generator by June 3rd (Birdsell and Kleber, 355).
These generators burned oil to produce a smokescreen, and were heavily used after the initial landings to obscure the beaches from aerial attack and to protect the "Mulberry" harbors during their construction. However, they were not used as a means of smoke generation during the initial landings.
At the American landings, smoke screens do not seem to have been used during initial combat. Kleber and Birdsell note that "Both the 30th and 31st Decontamination Companies saw action on Omaha Beach...with the missions of decontamination, smoke, and supply. At first, the platoon fought along side the infantry using small arms and grenades and later, when the beachhead was secured, it aided in evacuating wounded and in clearing Mine fields. During the afternoon the portable generators that had been lost in the surf at the time of the landings were retrieved and put into operating condition. As at Utah, there were no calls for smoke" (Birdsell and Kleber, 357).
Colin Kitching served as a Lieutenant in command of an LCP (Landing Craft, Personnel) at Sword Beach, where "LCPs were unsuitable for landing assault troops and we were switched to carrying out specialist smoke-laying duties." Much like the aerial smoke-laying units, he notes that their mission "was to provide smoke-screen cover for amphibious tanks in Juno landing area and for some of the bombarding warships" (Kitching). On Gold Beach, "from 0545 smoke shells were used to baffle the enemy's long range guns" (Holborn, 116-117).
Because of weather conditions and the immense logistical issues of the massive invasion, smoke screens were not much-used on a tactical level. They would have obscured the beaches from supporting naval artillery fire and heightened the logistical issues of the landing. Instead, they were reserved for use to protect supporting units and the naval armada from German artillery fire and aerial assault. Smoke screens were also intended to be used as a countermeasure for gas warfare, but the need for this never arose.
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