Carrying useless equipment just slows you down.
Carrying useful equipment also slows you down.
And things tend to be useful for only one specific situation anyway, so after you use them it's clearly in your best interests to discard them.
Commentary by memnarch (who has not seen the movie)
Knowing Zeppo, he'd probably had some idea of surprising the first trooper that would open the door and wrapping the jacket around their head for some reason. And in this case, improvising probably means stealing another ship of some kind. Stealing a ship seems unlikely to happen; or at least, I hope it wouldn't mean the Falcon gets left behind with the MacGuffin Modulator.
Problem solving by creating new problems that aren't his? Oh no; it's a sign! Zeppo's turning into management! This is going to make Finn's job of betraying the Resistance much easier if Zeppo keeps this up. Though actually..... maybe that's not the case any more? With that scene, it's hard to tell at the moment here if Finn is actually still a traitor or is in that spot where he thinks nobody is on his side, so everyone else is fair game for backstabbing.
Zeppo: I toss my snow jacket. Won’t need that any more.
Finn: What about when we go back to the Falcon?
Zeppo: Eh, I’ll improvise.
Chewbacca: Don’t even try to argue with him.
Zeppo: So, how do we find Rey?
Finn: Good question. General Phasma would probably know where she is.
Zeppo: Great! We find this General Plasma!
Finn: How are we going to do that?
Zeppo: I’ve already solved the problem. Don’t bring irrelevant details into it.