It's not absolutley necessary, but I find that it helps get my ideas organized.

If you have a film with dialog, it's a good idea to write a script so you can get the lines written down.

Yes, you should still write it down.
That way, your film will have more cohesiveness that if you just made everything up on the fly.
I tried to do that early on, and although it sorta worked, I find it's much better to write it all down.
You can also edit parts of the script, or get it reviewed by others much more easily if you have it all written down.
Trying to remember all the little details of the plot, sets needed, lines for voice actors, animation needed and everything else is just a pain. Writing it down doesn't take much of your time, and saves a lot of effort later down the road.

I'd recommend writing things down and plotting things beforehand. Even if you're making shorts where it's not really needed, it's  good habit to develop at this stage and it'll help you move on to bigger and better things more quickly.