If I use Nefarious Acolyte in Dominance phase to blank Withering Cold, would it cause to skip Standing phase anyway or Standing phase will take place? What is the exact timing?

Text from Nefarious Acolyte:

Action: Kneel Nefarious Acolyte and pay 1 gold to choose a plot card. Until the end of the phase, treat it as its printed text box were blank (except for Traits).

My ruling would be to proceed to Standing phase normally, as "At the end of the Dominance phase" the plot would stop being blanked. But I would like other opinion on this.

Ha!  Fair question!  Makes sense intuitively.
 
However, I do not think it would be blank, because the Acolyte's effect is only active 'until the end of the phase'. Thus, there is no point in time in which the Standing Phase could theoretically start happening and The Withering Cold is blank.

If the RRG specified a relevant part of the Dominance Phase (e.g. "Step 5: Transition to Standing Phase") then I would agree with you.  However, by the time the Standing Phase happens/doesn't-happen, the Acolyte is no longer active. 

FAQ "End of Phase Timing Sequence" says that after "until the end of the phase" lasting effects expire, there's a framework window for "at the end of the phase" delayed effects and reactions to them, occuring outside of any phase. During that window, the plot would not be blanked, and so the Standing phase would be skipped.

Now, one could argue that if there are no actual delayed effects resolving at the end of the Dominance phase, then the framework window between phases does not occur at all, and so the Standing phase should begin immediately. However, that would mean the general round sequence is dependent on certain cards being played (in unobvious ways), which would be very... clanky. I believe the void between phases exists regardless of the presence of delayed effects.