I know this thread is old, but since there isn't a lot of posts about The Sims and Linux (it's a niche in a niche) I thought it would be nice to bring an update.
It is possible to run TS4 under WINE, but is recommended to install with Lutris or Steam. According to
Lutris page, TS4 is rated Gold. Before you must install Origin, which isn't needed with Steam.
In my experience, the game runs flawlessly, except for screenshots in-game with 'c'. It takes a picture but the final result is something like this:
(this was taken in a home decor gig, showed glitched in all in-game thumbs, but in the revelation video the glitch disappeared)
When I screenshot with the system tool (Prtsc key) it works fine:
About Origin, I installed with Lutris, but had to change the prefixes to make it work as shown
here.
My game is heavily modded, graphics on ultra and runs smoothly. FPS isn't high (40-50 on live mode) 'cause my video card isn't great, but is totally worth imo.