Actually, the Punitive Expedition into Mexico is an interesting topic for gaming. US forces were mostly mounted, Uniforms would be the Montana hat, breeches, and leather leggings, with troops in shirtsleeves and ties, Pershing insisted on that. But, not only horses, there'd be trucks, Ford Model T scout cars, aircraft, and one or two armored cars.
For WW2, I would agree with the premise that Partisans would have used horses when possible. A horse is a flexible means of transport, regardless of location. Note US Special Forces troops with the Northern Alliance in Afghanistan. They found them quite handy for use in the mountains. Partisans did use horses initially in Barbarossa according to Paul Carrell's book "Hitler Moves East". Horses were simply transportation, and were, in many cases the difference between life and death as to who got away if surprised, and who got caught or shot. I, for one can see the probability of more mounted units for WW2.