DEICE and dispatch suggesting a derate later, our policy is to have no denates after DEICE/ANTIICE
There is no technical reason why one would not be able to use derated or even assumed thrust when having been deiced.
There are a variety of reasons for deicing requirements, but it is the runway conditions rather than the deicing requirement which allow/prohibit derated and ATM usage.
The difference of the OP's question/answer is the difference between Slippery/Contaminated runway characteristics, basically as summed up by previous poster.
Compacted snow can be seen as a slippery surface, whereas dry snow seen as a contamination form of the runway. In both cases performance should be assessed individually based on actual runway conditions and never be less then WET capability.