Horses (yet again)
Many months ago a poster here brought up the brilliant point that there wouldn't be all that many horses in Poland and probably not enough for cavalry units. I did some "research" since then and found that Poland actually had several state horse studs and Polish race horses were an important vector of western funds. In The Second World War these studs were moved east and then south for safety to save them from the Germans. They did actually fall into their hands but it seems obvious to me that this would probably happen again. The obvious upshot of this is that horse units are raised in the east and sent west using Russian and Polish breed-stock. This saves them from the worst of the chemical warfare. Similarly cavalry units in NATO are raised from French and Spanish stocks (if you ignore the stupid French stab-in-the-back theory) and are moved east and this is where the horse studs are.
Now, this all might seem useless trivia but it does give us some useful information. Cavalry units after the general collapse might even furtively trade across enemy lines for instance. Also horse stocks are rife for raid-and-capture and a scenario of troops raiding across the Oder to grab mounts if your supply line to your mount resupply collapses.
As we've discussed earlier horses actually do not run on grass. If you want grass-fed horses you need something on the order of seven remounts per trooper as horses are rested. Cavalry work is hard going for horses and historically in pre-modern armies fodder took up the bulk of logistical space as horses need high energy feed. There's also the annoying thing that horses won't graze in strange territory after dark even if fodder is their supplement. This gives you in idea of why horses with their higher land speed don't cover as much ground as infantry; horses move more quickly but for a shorter time. Also if you're running a cavalry game then unlike in the infantry game clean water becomes an issue. Horses drink about 30 litres to 50 litres a day, we can say 30 litres if resting and 50 litres if working. This water has to be clean. So a careful scouting route has to be made and water sources reconnoitred.
Although we tend to think of cavalry as just a few guys on horseback and maybe a packhorse or two, in an actual unit this will be different. The best example of this is going to be European cavalry units serving in the Second World War. For scenario and campaign ideas here's a Lone Sentry article on soviet cavalry from the early 1940s.
http://www.lonesentry.com/articles/cavalry/