In an e-mail to close colleagues, I would like to ask "How are you doing today?" in the beginning part. But till when is it natural to begin in this way? For example, I need to report one minor thing to a close colleague at 6PM as a first contact during the day. Can I ask this though it is already 6PM? I would like to say something to imply I care you personally, and to imply my interest is not only business with you. Is there any better expression? Thanks in advance.
I'd be inclined not to phrase it as a question, but rather something like:
'[I] hope you are doing well'
'[I] hope your day is going well'.
This seems a little less awkward and a little more natural in an email context.
As for the 6PM dilemma, I think you're right that it might be better to say something like 'I hope your day has gone well' instead of the second suggestion above. However, 'I hope you're doing well' will work at any time.