It seems like rolling resistance would tend to be negligible for these conditions for both its very low magnitude, and this tendency toward canceling.I did a quick and dirty calculation. Front wheel supports half of the cycle+rider mass: 70 kg or 700 N.
Add to that the 10 kg of the plate and we are up to 800 N.
Multiply by the coefficient of friction of 0.18 to yield 144 N.
Front wheel force is equal to half of the 400 N total rolling resistance. So that is 200 N.
200 N > 144 N, so this seems to be sufficient for the plate to slip on the ice.
Mind you, 200 N rolling resistance for a 700 N load is indeed ludicrously high. Thirty percent would be about right for a car on sand. A motorcycle on ice should be more like one percent. Reference here
[The calculation is for the case in which air resistance is negligible and the 400 N retarding effect is entirely from rolling resistance]