There is little known about bicycle snow plows on the Internet. Mostly it is an experimental project. Build something, tweak it, make changes and retest.
Bicycle snowplowing has some limitation that need to be considered. For one, traction on the bicycle even with studded tires is limited. Then there is the consideration of how much power is required to pull a plow. There is also the snow to consider. The heavier, deeper, and wetter the snow, the more power is required and vice-versa, the lighter and shallower the snow, the wider the blade for the same power.
The first version used a 1 foot high by 18 inch long blades hinged together with 2 door hinges and a threaded bar to spread the plow to a wider width. Heavy snow required reducing the length of the plow blades to 12". The threaded rod didn't work so well since it took forever to adjust the width so a triangle was used instead of a rod to spread the blades apart.
At first there were no wheels on the plow. A metal edge was bolted to the bottom of the plywood and scraped the ground. A 2X2 was used to bolt the plow to the chain stay of the bike but repeatedly cracked and broke. It did however keep the plow from fishtailing but when the bike was banked one of the blades would lift, resulting in a groove being plowed instead of a wide track through the snow. Still, it was wide enough to cycle in. The next design change was to chop the 2X2 and use a piece of rope to connect the plow to the towbar. This allows the plow to tilt and remain flat on the ground while reducing the stresses that cause the 2X2 to break. We'll see if it works better.
Warmer weather and a shovel allowed the pathway to be cleared except for a few icy spots. Then fluffier snow fell and having to cut a narrow width groove through the snow required far too many passes to clear a 2 foot wide path. With the dryer snow, not as much power would be required to pull the plow so a couple of pieces of plywood were screwed on to widen plowed the width to 32 inches.
As you can see from the photo, in fresh snow, the added wheels and blade width worked very well while test pulling the plow. Effort was very low and far easier and faster than shoveling. With the wider width it was even faster to clear a wide furrow. It took quite a few treks back and forth on a 8 foot wide pathway to clear it entirely of snow. V-shaped plows cut a fast groove in the snow but trying to push snow to the side doesn't work as the plow is free to slide sideways. It can be done though. The fastest way to clear the pathway is to do 3 passes with a ridge of snow between them.