MWM, I think that we all have these feelings from time to time. We can't see each others' faces or hear tones of voice. I don't think you come across as cold. I'm sure we all feel that way about the things that we say about ourselves and to each other sometimes, but we wouldn't be here for all of these years day in and day out if we didn't care. I think that at times we can all be gentle, or kind, or blunt, but I also think that by coming back to look after each other even when we have to hear or say something we don't want to hear or say, we show how much we care.
Don't let yourself overthink this. If you come here with kindness in your heart, this is where you belong.