No you can't reuse code from winforms in WPF.
and even if you could, you shouldn't.
whatever you can do with XAML, you can also do without it
You should really use XAML to define the UI, and then use DataBinding and MVVM, which is a much more professional way of development than the traditional procedural winforms approach.
Not using XAML is much more troublesome than using it. It may look intimidating at first but it's a really awesome thing to work with.
Of course that you don't have any XAML when using Winforms
No, of course not. winforms is a really old technology that doesn't support anything. That's why they created the Visual Studio designer, otherwise no one would have ever used winforms for anything, because of the horrendous gargantuan behemoth amount of code required to do anything useful.
Can I use the same code for the WPF application that I used for the
winforms application and get the same result?
Probably, by adapting some class names and whatnot, but then you lose the main advantage provided by WPF, which is precisely getting rid of the horrible winforms-like code.
considering the past experience using Winforms, should I somehow
change the way I'm thinking about design and implementation that
worked for Winforms but are not that appropriate for WPF?
Yes. WPF supports MVVM, and that requires a really different mentality from the traditional winforms approach.
I strongly recommend reading Rachel's Excellent Post about upgrading from winforms to WPF.