This does not work in the real world for bigger units however.
Because horses are no machines but animals, like humans, who can get exhausted too. There is one school of thought among military historians even which has the opinion that big groups on horses cannot move faster than pure infantry for longer periods of times. Namely because horses get exhausted more than humans through constant marches and have to rest longer to regain power.
I'm not really convinced of this. When reading 19th/20th c. AD military cavalry manuals, they calculate with a higher marching capacity of pure cavalry groups for an extended period of times. And I'm positive that they knew a bit about what they wrote in the official manuals.
But I never noticed that a mix of cavalry and infantry could march faster than with infantry speed anywhere in history. It's a kind of magic in BL, so.
While I'm a stern enemy of the whole cavalry marching bonus for mixed parties, I would not appreciate such changes. Why should cavalry march slower in woods or in snow? If the forests wood be so dense, also infantry might not be able to pass at all. And in deeper snow being on a horse might even be (much) better than having to plow through the snow by foot.