I'm not even quite sure I understand what you're describing, but it sounds like this:

You have speakers which already have wire attached to them. You say they're "bare wire", though if they are truly bare, they'll oxidize (rust) pretty quickly, so I suspect there really is a sheath around them or you'll be replacing those cables soon.

You have a subwoofer that is part of a surround-sound system ("home theater in a box"). The subwoofer has two connections marked "AUX INPUT". And you want to know if you can connect these speakers to the AUX INPUT.

The short answer is that you can't. "Input" means that an electrical signal is coming from somewhere and going into the subwoofer. You need a signal coming out of the subwoofer (or out of something) to go to the outdoor speakers. There might be something on the surround-sound system labeled "OUTPUT" that is not being used now. You might be able to run cable from that connection to the speakers. But then there is the question of what that signal sounds like and whether it's too powerful or not powerful enough for the speakers you have outside.