I have been fighting this problem for years. I am still working on it. Two things you can do to delay the freeze. Insulate the pipes, insulate the walls and seal the air leak. The cold air blast from a air leak from outside cold air on the pipe is like a "anti" blow torch. Seal any cracks. Wrap the pipes in insulatings, as thicj as you can find the insulation. Insulate the back side of the sink cabinet wall if that wall is the outside wall. Insulate the walls of the cabinet. If opening the cabinet doors is undesirable, then put a low wattage lamp under the sink. The heat will warm the space.
All that is assuming the freeze location is at the pipes under the sink. For my case, the freeze is at the pipes that ran under the floor before they reach the sink cabinet. I know because I can clear the clog pipe with a hair dryer at the space at the basement foundation floor and the joist cavity where the pipes ran (my kitchen is built on an enclosed porch).
If your pipes are ran inside an outside wall, they are at risk. There is not much space bwtween the pipe and the very outer layer of the wall for any substancial insulation. Rerouting the pipe may be your only option.