Heavy infantry and cavalry (and artillery, etc) are a function of many factors:
- Availability of weapons and horses
- Capabilities of the opponent
- Wealth available to pay for the forces
You can certainly march a column of cavalry and heavy infantry through a jungle and across rivers. All armies can do that. But it's a wise action only if that's the appropriate force to win the fight at the end of the march.
Other answers have already talked about Terrain and Availability of weapons and horses.
The capabilities of the opponent are obviously important. An enemy lacking anti-horse technologies will be (literally) overrun by your cavalry. Conversely, an enemy with a walled city and complex defenses requires your force to be much more sophisticated, and to include artillery and engineers...and perhaps allies.
Even small expeditionary forces require great wealth to gather, equip, and sustain. Those soldiers won't train and pay themselves, their weapons and armor don't grow on trees, trained warhorses don't pop out of every paddock, food doesn't grow along the line of march in the quantities you need, etc. The promise of looting won't keep good soldiers for very long. European conquerors brought all the firepower they could afford. If they could have afforded more, they would have brought it.