AC 25-13 - Reduced and Derated Takeoff Thrust (Power) Procedures
5. f. The AFM states, as a limitation, that takeoffs utilizing reduced takeoff
thrust settings:
(1) Are not authorized on runways contaminated with standing water,
snow, slush, or ice, and are not authorized on wet runways unless suitable
performance accountability is made for the increased stopping distance on the
wet surface.
So the AC makes an absolute prohibition against using reduced thrust for contaminated runways. No such limitation applies for derated thrust, which is essentially treated as if the aircraft had been built/certified only with that lower thrust level.
Bear in mind in this context that the FAA's handling of contaminated runways is somewhat less sophisticated than that of some other authorities.