In Germany flight duty time regulations also apply to employed pilots flying without AOC. There is no exemption for that.
If they really used Type I Fluid for anti-icing, they had a holdover time of 2 to 4 minutes (at below -10°C and snow). They also had to consider AEA cautions:
CAUTION: Heavy precipitation rates or high moisture content, high wind velocity or jet blast may reduce holdover time below the lowest time stated in the range. Holdover time may also be reduced when aircraft skin temperature is lower than OAT. Therefore, the indicated times should be used only in conjunction with a pre-takeoff check.
and
CAUTION: Wing skin temperatures may be lower than OAT. If this condition is identified, a stronger mix (more glycol) may need to be used to ensure a sufficient freeze point buffer.
That is not working in given conditions unless you anti-ice at the threshold immediately before takeoff.