I added the .ico file to my project, setting the Build Action to Embedded Resource. I specified the path to that file as the project's icon in the project settings, and then I used the code below in the form's constructor to share it. This way, I don't need to maintain a resources file anywhere with copies of the icon. All I need to do to update it is to replace the file.
var exe = System.Reflection.Assembly.GetExecutingAssembly();
var iconStream = exe.GetManifestResourceStream("Namespace.IconName.ico");
if (iconStream != null) Icon = new Icon(iconStream);