Mountain divisions arent that useful, because not all countries are full of mountains plus for my CoW career i never had a big battle on the mountains. It was always on the plain or atleast at the hills. Imagine you sending one to the ie. Alps, and you get intercepted by a regular infantry near Vienna? Consider me neutral for the cavarly, im too stupid to talk much, so i will let more professional and experienced guys give their word.

Commandos are powerful mountain units. So, don't need mountain divisions.
Cavalry: Infantry have machine guns which would chew up cavalry. Cavalry would be faster than infantry for short distances. Horses need to rest too.
Horses seldom will gallop more than 1.5 or 3 kilometres (0.93 or 1.86 mi) before they need to rest, though horses can sustain a moderately paced gallop for longer distances before they become winded and have to slow down. A horse would not be able to cover as much territory as a light tank. So, cavalry would be faster than infantry and slower than a tank. You aren't going to be able to get horses to improve their speed on the battle field. So, no speed upgrades. Cavalry stats for attack and defense should be weaker than infantry. Infantry have some machine guns and automatic rifles which tear up infantry. " the Germans' widespread use of automatic weapons, especially the Sturmgewehr 44 assault rifle, the select-fire M2 carbine was introduced, along with a new 30-round magazine. The M2 had a fully automatic rate-of-fire of about 850–900 rounds-per-minute. Although actual M2 production began late in the war (April 1945), US Ordnance issued conversion-part kits to allow field conversion of semi-auto M1 carbines to the selective-fire M2 configuration. These converted M1/M2 select-fire carbines saw limited combat service in Europe, primarily during the final Allied advance into Germany. In the Pacific, both converted and original M2 carbines saw limited use in the last days of the fighting in the Philippines.^[" "The Horse Cavalry rifle platoon consisted of three rifle squads and a platoon headquarters. The platoon hq consisted of a lieutenant as platoon leader, a platoon sergeant, a file closer sergeant, two intelligence scouts, who also acted as messengers, and three basic privates, who replaced squad casualties.
The last horse cavalry charge by a U.S. Army cavalry unit took place against Japanese forces during the fighting in the Bataan Peninsula, Philippines, in the village of Morong on 16 January 1942, by the 26th Cavalry Regiment of the Philippine Scouts. Shortly thereafter, the besieged combined United States-Philippine forces were forced to slaughter their horses for food and the 26th Regiment fought on foot or in whatever scarce vehicles were available until their surrender.
The 10th Mountain Cavalry Reconnaissance Troop of the 10th Mountain Division, while not designated as U.S. Cavalry, conducted the last horse-mounted charge of any Army organization while engaged in Austria in 1945.^[9] An impromptu pistol charge by the Third Platoon was carried out when the Troop encountered a machine gun nest in an Italian village/town sometime between 14–23 April 1945." So, cavalry in WWII were generally weaker than infantry most of the time. Infantry rifles had greater range. Cavalry generally used pistols with shorter range than rifles. Cavalry generally had to get pretty close to their targets. Infantry could shoot the horses from under them. So, cavalry horses should be weaker than infantry.