The following example traps the Application.OnShowHint event and changes the font.

Example:
type
  TForm  = class(TForm)
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    procedure MyShowHint(var HintStr: string;
                         var CanShow: Boolean;
                         var HintInfo: THintInfo);
    { Public declarations }
  end;
var
  Form : TForm ;
implementation
{$R *.DFM}
procedure TForm .MyShowHint(var HintStr: string;
                            var CanShow: Boolean;
                            var HintInfo: THintInfo);
var
  i : integer;
begin
  for i := 0 to Application.ComponentCount -   do
    if Application.Components[i] is THintWindow then
      with THintWindow(Application.Components[i]).Canvas do begin
        Font.Name   := 'Arial';
        Font.Size   :=  8;
        Font.Style  := [fsBold];
        HintInfo.HintColor := clWhite;
      end;
end;
procedure TForm .FormCreate(Sender: TObject);
begin
  Application.OnShowHint := MyShowHint;
end;