Holdover times
ACARS (now where have I come across that acronym!), It's not an exact science, unfortunately... Just to take one obvious example, your idea of "very heavy snow" might not be the same as mine, or the crew's. It's all rather subjective.
There are tables, however, giving estimates of safe "hold-over" times, for the crew's guidance. This varies according to the method of de-icing (or anti-icing) that was used, the temperature, and the subsequent type of precipitation (if any). The recommended maximum time is then added to the time the de-icing procedure was STARTED.
Wing anti-ice only heats parts of the leading edges, and is not for use on the ground. A "light covering" on the wings is an issue. Never take-off on the assumption that snow on the controls will blow away, whether you are in a light aeroplane or an A380.
If in doubt, de-ice again. But most of the passengers will not be impressed... Particularly if you are already much delayed, reaching the crew duty-hours limit, and the extra delay means you have to cancel the flight. Tricky decision, isn't it?