Only issue with Cold Weather Equipment is I don't believe you receive it on the Republic side at all. I know I did get it on my Sorcerer however.
Hmm this reminded me about the future requirements for obtaining HK-51.
"The only thing we’re saying today is its going to take a serious amount of work, involves a galaxy-wide mission, introduces some different ways of playing the game and most people will need to have a 50 of one faction and at least a mid-level character from the other faction. Get working on those Legacy characters!" - Daniel Erickson (Lead Game Designer)
This would fulfill the mentioned level 50 and mid-level character for Republic players but not Imperials with a 50.
Also the HK-51's ship crashed on Belsavis, a planet with a significant Dread Masters storyline for the Imperial side.