If you want for this member to be databindable by either Winform or WPF, I believe that you need to declare it as a property.  I'm about 95 percent positive that databinding requires a property (getter/setting syntax).  I have a small wpf solution that demonstrates this, but I don't see a way to attach it here.
Here's the code: (built with VS 2008 SP1, targeting .net 3.5 - I used a WPF Project).
There are 2 items in the WPF project, the main window (window1), and the object that we are testing (DataObject)
There is a label on the window that is databound to the Name property in an instance of data object.  If you convert the Name property to a field (remove the getter/setter), the databinding will stop working.
Window1.xaml:
<Window x:Class="WpfDatabinding.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Grid>
    <Label Name ="Label1" Height="28" Margin="12,24,37,0" VerticalAlignment="Top" Content="{Binding Name}"></Label>
</Grid>
Window1.xaml.cs
using System;
using System.Windows;
namespace WpfDatabinding
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        private DataObject ADataObject;
        public Window1()
        {
            InitializeComponent();
            this.ADataObject = new DataObject();
            this.ADataObject.Name = "Hello!";
            this.DataContext = this.ADataObject;
        }
    }
}
namespace WpfDatabinding
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        private DataObject ADataObject;
        public Window1()
        {
            InitializeComponent();
            this.ADataObject = new DataObject();
            this.ADataObject.Name = "Hello!";
            this.DataContext = this.ADataObject;
        }
    }
}
DataObject.cs:
namespace WpfDatabinding
{
    public class DataObject
    {
        // convert this to a field, and databinding will stop working
        public string Name
        {
            get;
            set;
        }
    }
}