I just tested adding the following stuff to the war3mapSkin.txt file (Some random font in the mpq). It altered the game font from the time said map finished loading to the time another map finished loading. (Including the out of map menus).
war3mapSkin.txt:
[CustomSkin]
MasterFont=Fonts\tt5500m_.ttf
MessageFont=Fonts\tt5500m_.ttf
ChatFont=Fonts\tt5500m_.ttf
EscMenuTextFont=Fonts\tt5500m_.ttf
InfoPanelTextFont=Fonts\tt5500m_.ttf
TextTagFont=Fonts\tt5500m_.ttf |
Edit: Same result with an imported font:


Edit2: The fonts for chat messages and floating text don't get reloaded at map initialization, so ChatFont and TextTagFont will do nothing.