I am using Ubuntu Xenial with the MATE desktop enviroment.
I want to know if there is any way to change the theme of the alt+tab switcher. I do not want to replace my window manager, but am ok with installing packages.
32-bit system.

Hello,

have you checked here: https://community.linuxmint.com/tutorial/view/1395

This is for Mint with MATE, but I am fairly sure it applies for your Ubuntu MATE as well.

Thank you, but there is nothing on the alt tab switcher.

alt-tab is just another keyboard shortcut, which can be mapped to another application.
alternative window switchers exist (i know for a fact that rofi has that functionality, which is a little stark in appearance, but many more exist).

1 members found this post helpful.

It's a standard that bridges OSes. Deal with it. If you don't like the keystroke, then map some other key to do it. Or get one of those gaming keyboards with macro keys and map that to it. If it's the look of a thing in the desktop, then there's source code for that. If you're expecting a blog post or youtube tutorial on it, you're probably gonna fall short. Or run into dated references that no longer apply to the current sources. If you're wanting to do something more than change a color of something you'll have your work cut out for you IMO. But what do I know, I tend towards minimal-ist things where alt+tab changes focus ONLY. And alt+shift+tab changes it in the reverse order. Anything more and it's pixels waste at best, pixel, cpu, ram, and time waste at worst.

I'm not sure what you're talking about: the little box that pops up? How long do you have to look at it? If you don't want to see anything, use Alt-Esc!