16-bit applications can't run in long mode (i.e. a 64-bit OS), so you'll need a 32-bit OS to run these apps in WINE. WINE is just a shim and a library reimplementation, not an emulator, so it just passes the instructions on to the CPU, and you're limited by what the CPU can do.

Hmm... I wonder if you can run 16-bit applications in WINE on a 32-bit VirtualBox VM running on a 64-bit Linux system. That sounds like overkill, though. Might as well just use PCem or DOSbox, depending on your use case (PCem: cycle-accurate emulation of a whole PC, including specific hardware models and running any OS a real PC could; DOSbox: playing some old games for fun).

TBH, I'm not sure what win3mu's point is, either: it probably won't be open-source, and right now the only reason to not use PCem or DOSbox is if you don't own a legitimate copy of Win3.1 and you're not willing to pirate it. An open-source clone of Windows 3.1 that can run any Win16 program in long mode (by interpreting the instructions like an actual emulator) would be a great idea, but this isn't it.