Properly written Win16 applications are agnostic with respect to memory protection. Windows 3.0 could run in real mode (8086+), standard mode (80286+), or enhanced mode (80386+). Enhanced mode used V86 mode, which didn’t exist on the 80286, to support DOS console windows. In standard mode, Windows suspended itself to allow running DOS applications.

Real mode support was in fact dropped in Windows 3.1, so any program that runs under that is guaranteed to run under Linux/Wine (though not guaranteed not to crash because of some unimplemented API).

In protected mode, all Win16 code runs in ring 1 or 3, including all drivers and application programs, as well as the so-called ‘kernel’, which is just a shared library that provides support for coroutines, among other things. The actual kernel that runs in ring 0 is the DPMI host.

Memory segmentation is 100% supported on AMD64 in compatibility mode. This is entirely independent of the default operand size: it is purely a historical coincidence that 32-bit code segments tend to go hand-in-hand with flat memory models.