A somewhat rare place for battle to happen, but still very possible. Depending on the rivier itself, it may forbid passage for trucks and even halftracks. worst case scenario is that only tanks can cross the river. To see what can and cannot cross, press F2 while having a unit selected (preferable only one type). Green areas are fully passable, reddish areas are difficult to traverse, but still possible if given some time, while purple areas are not passable at all.
Any player that gets caught while passing through a river is in deep trouble, as they are at a height and speed disadvantage. Tanks get caught by tank destroyers with their pants down, unable to avoid the projectile no matter where they turn. Spending any time in the water is a risk not worth taking, but if you must, there are ways to make the pain not last as long.
First, be sure you have plenty of infantry to send, as some will likely not make it across at all and you need to have some force to secure your ground later. Second, have some support weapons for your infantry. These are often tanks, as they are, more or less, universal in application, but howitzers are even better, as you don't risk losing them for attempting a crossing.
For examples of these evil lands, check the map "moro river" for Spring:1944, on the left side of the map. Crossing that territory is often sucidal, while at the same time giving very powerful attack angles if a crossing should succeed.