Adding icon to left of DropDownButton (expanded) in flutter

Use DropdownButtonFormField as it has decoration property. You can use prefixIcon attribute to set icon on left side.

Example:

DropdownButtonFormField<String>(
         decoration: InputDecoration(
         prefixIcon: Icon(Icons.person),
         ),
         hint: Text('Please choose account type'),
         items: <String>['A', 'B', 'C', 'D'].map((String value) {
         return DropdownMenuItem<String>(
         value: value,
         child: new Text(value),
       );
      }).toList(),
     onChanged: (_) {},
),

Result:

Remember, everything is a widget, so:

iconSize: 0,
hint: Row(
         children: [
            Container(
                child: Text('Freguesias'),
            ),
            Container(
                child: Icon(Icons.arrow_drop_down),
            ),
          ],
 ),

This may too late. But will helpful for upcoming viewers.

Instead of using DropDownButton, we can use DropDownButtonFormField. Which has a decoration property. With this we can make use of prefixIcon property to add icon to the left side of DropDownButton:

DropDownButtonFormField(
  decoration: InputDecoration(
    prefixIcon: Icon(Icons.person, color: Colors.redAccent),
  ),
  ...
);

try to use decoration property of DropdownButtonFormField and use prefixIcon property.

DropdownButtonFormField(
      isDense: false,
      itemHeight: 48,
      isExpanded: true,
      decoration: InputDecoration(
        prefixIcon: Icon(Icons.question_answer_rounded),//Add this line
        filled: true,
        ...
        ),
        ...
  )
        

This will add an icon at left.

If the icon really should be visually part of the DropDown component, you could go the following route. Its a bit hacky and lacks being responsive but its a start for some more experiments. I added a complete working example so you can copy paste it to a runnable main dart file.

In a nutshell, it uses a Stack layout so the icon is just placed over the dropdown component. Then i padded the Text so that there is space to the left.

void main() => runApp(MyApp());

/// This Widget is the main application widget.
class MyApp extends StatelessWidget {
  static const String _title = 'Flutter Code Sample';

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: _title,
      home: Scaffold(
        appBar: AppBar(title: const Text(_title)),
        body: MyStatefulWidget(),
      ),
    );
  }
}

class MyStatefulWidget extends StatefulWidget {
  MyStatefulWidget({Key key}) : super(key: key);

  @override
  _MyStatefulWidgetState createState() => _MyStatefulWidgetState();
}

class _MyStatefulWidgetState extends State<MyStatefulWidget> {
  String dropdownValue = 'One';

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: Stack(
          children: <Widget>[
            DropdownButton<String>(
              value: dropdownValue,
              //icon: Icon(Icons.arrow_downward),
              iconSize: 24,
              elevation: 16,
              style: TextStyle(color: Colors.deepPurple),
              underline: Container(
                height: 2,
                color: Colors.deepPurpleAccent,
              ),
              onChanged: (String newValue) {
                setState(() {
                  dropdownValue = newValue;
                });
              },
              items: <String>['One', 'Two', 'Free', 'Four']
                  .map<DropdownMenuItem<String>>((String value) {
                return DropdownMenuItem<String>(
                  value: value,
                  child: Padding(
                    padding: const EdgeInsets.only(left: 30.0),
                    child: Text("$value"),
                  ),
                );
              }).toList(),
            ),
            Container(
                margin: EdgeInsets.symmetric(vertical: 10),
                child: Icon(Icons.arrow_downward)),
          ],
        ),
      ),
    );
  }
}

Wrapping your icon and dropdown widget inside a row widget, nested inside a container will do the work like below:

body: Container(
    margin: EdgeInsets.only(top: 64.0, left: 16.0, right: 16.0),
    color: Colors.white,
    child: 
    child: Row(
    children: <Widget>[
      Icon(
        Icons.person,
        color: Colors.redAccent,
        size: 20.09,
     ),
     Expanded(
        flex:1,
        child:DropdownButton(
            isExpanded: true,
            items: _studentList.map((val) {
            return DropdownMenuItem(
              value: val,
              child: Text(val),
            );
        }).toList(),
        value: _currentSelectedItem,
        onChanged: (value) {
         setState(() {
           _currentSelectedItem = value;
         });
      },
     ),
    )
  ]  
)

Simple way to do this would be to pass child prop to DropdownMenuItem, you can then pass any widget, i have created a row and passed the icon and text in the row :

items: <String>['George Green School', 'George Blue School', 'George Red School', 'George Yellow School']
                .map<DropdownMenuItem<String>>((String value) {
              return DropdownMenuItem<String>(
                value: value,
                child: Row(
                  children: [
                    Icon(Icons.dangerous),
                    Text(value, style: TextStyle(fontSize : 12),),
                  ],
                ),
              );
            }).toList(),