I live in Norway and after 20 years in a ski troop I got an opinion about winter war. First, if you want a winter rule, you need terrain rules too, because snow and cold have different effects on different terrain.
Lets take Finland, now that is a terrain with forest, lakes, marshes and swamps, making it impassable during summer. Historically correct, most of the campaigns and fighting in Finland from 1600 to WWII have been during winter, when the lakes and marshes are frozen. In Norway it is opposite, because Norway is all mountains, and during winter the mountains are impassable. So if you want a winter rule that is not insane, you will need to make territory specific terrain, and a season rule that effects specific terrain different.
Combat during winter is different from summer. During winter the minefield is covered by snow and wont stop anybody, but since the attacker move slow in snow, the defensive mg-fire makes more impact. Artillery barrage is useless since the shells got buried in the snow. The exception is when the enemy attack over a frozen lake, then artillery barrage will break the ice and the attackers will be drown in the cold water. I will say that the winter favor the defender, since he can sit in a blockhouse or pillbox and keep warm, while the attacker is out in the cold and get frostbite. Statistics show that during winter combat half of the casualties is due to frostbite. During summer combat only a few % come from sickness, and most from battle wounds. The exception is of course the ski troops, that can make long range surprise attacks during winter, but only if the terrain is forest.
Another impact from winter is the higher fuel consumption. A truck that used so much fuel on the German highway during summer, that same truck used seven times more fuel on a Russian dirt road during winter. That is a fact, and some officers at the Academy even claim that was the main reason the German attack on Moscow got bugged down in November 1941, the Germans was out of fuel. Analyses of the Barbarossa battles indicates that the German combat ratios were the same all the time, and that snow and cold did not effect the German combat effectiveness, but the trucks failed to supply the army since they used 7 times more fuel on a Russian dirt road, and the generals had failed to include that in the plans. But since this A&A game don’t have any supply rules, it is hard to model this. But if you make a house rules that says you must pay some IPC for every attack, then let attacks during winter cost twice as much
About Amphibious Assaults, it is true that the D-day landings in Normandy could only be done on that specific day it was actually done, and because of that many wargames have a rule that let invasions be done in summer turn only. But in the real WWI and WWII a lot of Amphibious Assaults, raids and invasions were done both in winter and against mountain terrain, some of them here in Norway, so it would be stupid to make a rule that only allow invasions in summer. In that case you would need special rules for invasion of France.
Another issue is aircrafts. During a blizzard there would of course be no planes in the air, but if the weather is good then winter actually favor aircrafts. First, they can use frozen lakes as airfields and allow for more sorties than during summer when they have to use hard surface airfields. But this is only in territories with marshes and mountains, like Norway and Finland, where there are few corn fields but many lakes. In France and Germany it is opposite. Also it is more difficult to hide from aircrafts during winter, since your tracks in the snow will blow your position, and so will the smoke from your bonfire.
all for now,