At what point would a 2nd De-ice normally be needed?
When there is any ice accumulating on the wings
It is save to say that after engine start, heaters etc take care of ice?
No. On a B737-700 only part of the leading edge of the main wing is heated.
Is snow covering a concern on wings/control surfaces?
Yes.
but I assume a light covering is not an issue.
It very much is an issue.
Most if not all airlines operate on a 'clean wing' policy. That is, no ice/snow/slush/frost/etc whatsoever allowed on the wings and tail. A bit of frost on the fuselage might be ok.
I would assume you were initially de-iced, and then another treatment took place called anti-ice.
Depending on the type of fluid used, the temperature and the conditions at the time this will give a certain 'hold over period', a time during which new built up should not occur. In addition, the flight crew will have (should have?) checked for contamination prior to take off.
If all checks are ok, you go. if not, you go back and de-ice/anti-ice again.