I have now tried out SpritePad 3.52 and it works :-)
I was and still is using the W64 version.
BTW, you can also install winetricks and then isntall .NET. What I did was run "winetricks dotnet45" and after that, I can run the .NET versions with just a "wine Char...."
Correction...
It seems SpritePad 3.52 is not working for me with .NET in Wine. However, the W64 version works with:
wine64 SpritePadC64Pro_W64.exe
Not sure why the .NET version doesn't work but it does with CharPad.