For Soviets, every third sapper platoon in the regiment's engineer company was also performing minelaying activities. These could be equipped with certain models of APCs or trucks towing PMR-3 or PMZ-4 mine laying systems or truck-based UMZ scatterable mine system. GMZ tracked mine-laying vehicles were also common. All of them were used with intent to mechanise and speed up otherwise labour-intensive, time-consuming minelaying process. With an exception of UMZ, adopted by the Soviet Army in the early 1980s and consisting of six individual launcher units each containing 30 tubes on truck chassis, all other systems are abstractly represented with existing minefields: speed of minelaying is irrelevant as it is something pre-planned.
US had GEMSS mine system (Ground Emplaced Mine Scattering System), replaced in US service by the Volcano mine system. The mines were deployed from either the towed M128 "Frisbee Flinger" (first fielded in June 1985 but production problems led to numerous delays, so it entered service around 1986) and the M138 "Flipper" portable mine layer (entered service around 1991). They were not such a common sight (69 deployed?) and were soon replaced by Volcano system, which however is out of current Armored brigade timeframe.
British introduced Ranger scatterable mine system in 1976, which was a mix of both methods. While it could be mounted on a variety of platforms, usually an FV432 would be fitted with a plough through which bar anti-tank mines would be laid. On top, the fully rotatable launcher would be installed with 1296 plastic anti-personal scatterable mines. As each section of the anti-tank minefield completed, several "barrels" of scatterable mines would be fired as cover.
In my personal opinion, such vehicles at the moment are not worth the delay necessary to implement them at this stage of game development. But you raised some interesting points. There used to be engineer class as a proposal, but it was never well defined as an idea and eventually dropped. I think the idea was to have infantry units dismantling mines and obstacles. Now, sappers could also deploy mines. Protective minefields are usually employed and emplaced at the small-unit level (platoon or company/team). The authority to emplace hasty protective minefields is normally delegated to the company/team commander, laid on short notice by units that use mines from their basic load or local stock. The mines are laid so that they are easy to detect and recover by the laying unit. Above that level, authority to emplace mines goes to higher echelons, at least in US documents I was able to read. But even hasty protective minefields would require some considerable time to deploy, which doesn't fit well with average "skirmish" type scenarios in this game, where the enemy is very near etc. so mines placed in a setup phase can handle the same job.
Another scatterable minefield delivery method, more widely available (effectively through whole Cold War), is by aircraft and helicopters. But, the issue of minefield deployment authority remains. I also wouldn't like to burden the player with micromanaging (unless necessary), and even more importantly we don't want to introduce systems dynamic AI is unable to use effectively without scripting.
But if you (or anybody else) have some engineering experience, feel free to share it. Many of the game cardinal mechanisms were built upon input and experience provided by people who served (or still do) and that is something hard to obtain from simply reading books or manuals.