My judgment for this has not always matched my fellow engineers. I generally defer to them if they have more primary responsibility for the answer after giving some argument. With that warning, my personal opinions:
1) MDMT is based on metal temperature, not process temperature. How cold would the metal pipe be using average temperature from inside of the wall to the outside for the section in question? Ambient air would warm the metal. The metal pipe has mass which will want to maintain the same temperature. Gas heat transfer to metal is not very high rate. How long would extra-cold process fluid flow in this section before operator made necessary adjustment?
2) With failed control valve, would the temperature of the gas after the valve decrease or increase? Would not the downstream gas be warmer with less pressure drop? Is the piping rated for the full pressure? Overpressure would be a greater concern than low temperature here.
3) If there were boiling liquid at the bottom of the pipe cross-section, then the hazard would be greater considering uneven cross-section temperatures.
4) MDMT is for metal temperature at a specific pressure. Lower pressure technically allows for colder metal temperature than MDMT. See the ASME Code for Pressure Piping, B31.3. Note particularly Fig. 323.2.2B "Reduction in Minimum Design Metal Temperature Without Impact Testing".
5) I think perhaps the concern is "the metal is normally cold, then the pressure increases which causes stress the piping is not designed for." If so, then assess the hazard. Reduce the maximum pressure if needed. Change piping material if needed.
6) The major suppliers of commercial nitrogen have standard designs for their storage and distribution systems. At some point, there will likely be a transition of material from stainless to carbon steel. When I did hazard assessment for plant distribution nitrogen systems using sch 40 carbon steel pipe, we evaluated each piping section spec for suitability to expected conditions. I do not remember specifically considering control valve failure, but that would have been one of the questions we answered.