Does it also mean cold-hearted?
yes, it can nean that as well, there is laso a song -" bo ze mnie taki zimny drań"
Does this mean you feel cold?
It means more like I feel you are cold (zimny- adjective)
Zimno ci/ Tobie jest zimno. you feel cold. (zimno- adverb)
To the touch or emotionally?
So it's like your skin is icy or something like that. Dzięki!!!
I like the intonation:
“Jesteś baardzo ziiimny~!”