I also "freeze" with emotions. (Its bad enough with grieving but if you do it when someone you feel attracted to comes on to you it totally ruins your day...)
With grieving I've never been able to comprehend the whole NT thing of "someone I work with has lost someone close lets say how sorry I am". The one time I lost someone close to me the last thing I wanted was a whole series of people reminding me of it and apologising for something that wasn't their fault. What I tend to do in that situation is just to ask "how are you feeling" in a way that makes it obvious that if they want to pour out their heart they can, but if they want to say "not too bad" and change the subject thats fine as well