Soldering a connection to a mini USB B port

I have a device that utilizes a USB Mini B, like the one pictured HERE. I can use that USB port to send the device some data through a computer.

My question is, is it feasible/possible to solder wires to that connection so that way I can send data to the device through an Arduino mini?

I basically want it so that it's as if I plugged my Arduino to that port.

Yes you can but it is tricky. You would be much better off using a connector that is already mounted on a PCB.

Breakout board