Unfortunately, the current answer is: you cannot (unless you figure out and modify the source code).

In this answer, I list the ways which do not work, to save future reader-modders the time and trouble of trying and failing.

A. Existing bug report

• Bug #756845 ("Unity dash search unable to change font/icon size") refers to this exact problem, as shown by part of the screenshot for the bug report:

  
  
  

  




• The bug has been confirmed and labeled "low importance", with no comments by developers or anyone else on a workaround or when it will be resolved.

B. Changing fonts or the scaling factor in gnome-tweak-tool

• This does not work either:

  
  
  

  




• Changing the scaling factor appears to change everything BUT the dash/hud font size (that's a 1920x1080 screenshot below -- compare the terminal font size!):

  
  
  

  

C. Editing dash-widgets.json in the Unity Theme folder

• You can find a file called dash-widgets.json in /usr/share/unity/5/ and /usr/share/unity/themes. This contains a bunch of CSS-like settings that may give you hope, such as:

  
  
  

    "preview-heading-small"  : {
  
  "main-title-size"    : 23.0,

  
  
  

  but changing them does not work. (the Dash font is approximately size 22)

D. Changing the Launcher Icon size Doesn't Affect It

• Since the dash text field is almost exactly the height of the Ubuntu launcher icon, you might think decreasing the icon size would change the height of the text field and make its font smaller.

  
  
  
  
  
  • Changing the icon size is easy from the Unity Plugin in CompizConfig Settings Manager (ccsm), or from its MyUnity frontend:
  
  
  
  
  

  
  

  
  
  
  
  
  • But decreasing to the minimum, 32, doesn't change the dash font size!