Is it possible to build bitcoin source code into a windows .exe file, using Ubuntu? I am using an ubuntu machine and have compiled the bitcoin source code a few times without issue. I am able to use bitcoin-qt just fine in the terminal to load the interface, but I'm wondering if I can make the code into a .exe file and put that file onto windows and run the client there without dependencies.

Is it possible to do that? Or will I have to install the dependencies on windows and compile in windows into a binary that requires no dependencies?
Yep you sure can instructions can be found at https://github.com/bitcoin/bitcoin/blob/master/doc/build-windows.md.

And the provided build scripts all use static linking so you end up with one big executable that does not require installing any dependencies on your Windows machine.