Before the launch of Battlefield 4, a lot of was made of the Frostbite 3 engine at its heart – this included dynamic wind/dust physics. However, in Battlefield 4 they appear to have been missing (or disabled) since launch.
These effects include trees moving due to wind from vehicle movement (helicopters, jets flying by, etc.) and more dust and wind when helicopters were landing on the ground, due to rotor movement.
Here is the official promotion video for Frostbite 3. Head to 56 seconds in to see these environmental effects in use.
And here’s a demonstration of explosives causing trees to move in Battlefield 3…
The same movement does not occur in Battlefield.
Anyway, it would appear that these were disabled by mistake and should make an appearance in the game in the next patch release.
They are indeed enabled (they were apparently disabled by mistake) – on the CTE, which means you’ll see them in the next patch release.
However, another DICE employee has stated that providing this to all users is “not a priority” at the moment.