If you work with Visual Studio then it is pretty easy to get persistable settings. Right click on the project in Solution Explorer and choose Properties. Select the Settings tab and click on the hyperlink if settings doesn't exist.
Use the Settings tab to create application settings. Visual Studio creates the files Settings.settings
and Settings.Designer.settings
that contain the singleton class Settings
inherited from ApplicationSettingsBase. You can access this class from your code to read/write application settings:
Properties.Settings.Default["SomeProperty"] = "Some Value";
Properties.Settings.Default.Save(); // Saves settings in application configuration file
This technique is applicable both for console, Windows Forms, and other project types.
Note that you need to set the scope property of your settings. If you select Application scope then Settings.Default.<your property> will be read-only.
Reference: How To: Write User Settings at Run Time with C# - Microsoft Docs
Best Answer
I think that there are two answers here... really just one answer to "Should I" and one answer to "Could I".
As far as "Could I", it is certainly possible. MVVM really just relies on a view that can bind to a view model. Since WinForms supports binding, this certainly is possible. You may need to write some code to make that binding more useful in an MVVM world, but it is (at least) theoretically possible. If it worked well, the benefits would be pretty great, IMO. You could make sure that your WinForms "View" had no UI behavior, except for creating the visual objects and binding them (in code, not declarative like in XAML). WinForms objects are very difficult to test, where ViewModels are very easy to test.
As far as your real question: "Should I", that becomes much more of a project-level decision. What are your goals? If you are looking to make some rather complex UI logic testable, then you might at least look into it. Fortunately, though, there are other patterns (Model-View-Presenter, for instance) that have more community backing that also has you write a testable "presenter" class. I find ViewModels significantly easier to write unit tests against compared to Presenters, but I think that is a personal preference.
Just as an aside, the MVVM pattern is mostly another name for the "Presenter Model" pattern. You might look to see if anyone is having success with the "Presenter Model" against WinForms UIs.
Good luck!