During the Cold War, was there any penalty for a US military officer entering into a personal friendship with their Soviet-bloc counterpart?

 The contact itself wasn't illegal or forbidden - but you'd better report it!  We were required to report any contact with any representative of the other side. 

If you fail to report it, you're automatically presumed to be attempting to cover up something illegal.

If you were an American, your FBI was responsible for counter-intelligence operations within the 50 states.  Outside the USA, it was your CIA.  For all you knew, the Soviet officer you were buddies with was being watched by one or the other, depending upon where you were.  Your own branch of the USA military would also have its own counter-intelligence organization, and you just might have the misfortune to have a colleague or neighbor mention something to them after seeing you and your pal together several times.

In other words, if you didn't inform your commander the day after you first met the guy, the next thing you knew you might be talking to the FBI or some plainclothes guys from your military department...and no matter what you and the Soviet guy talked about, or the nature of your relationship, you would already be in DEEP.

My guess is you could lose some security-clearance if you immediately reported it, or lose your job and face time in prison if you didn't report it

i would hope not

Consorting with the enemy. 

I don't know; I don't even know how they would manage that, because the USSR was very strict during the Cold War, preventing contact between Soviets and Americans.