Can Mei's Ice Wall be destroyed by players?

I've seen Mei's Ice Wall get destroyed when they use it in front of the cart, the cart just smashes through the middle, leaving a pillar of ice on each side left standing.

And that got me wondering, is there any way players can destroy an enemy Mei's wall prematurely?

Yes. According to personal experience and Furious Paul's Overwatch Strategy Guide, where it says:

Ice Walls consist of 5 pillars right next to each other. Each pillar has its own hitpoints of 500

meaning, that they can be destroyed. Alternatively, they also get destroyed after either

The Mei that placed them cancels them
or
after 4.5 seconds.

And it also says that:

Ice Walls do not block Payloads, as they will be able to continue moving through it.