I've spent the past couple days struggling to get Origin, and The Sims running in Wine/PlayOnLinux.
I thought I'd share the tips that helped me.
I installed Origin into a 32-bit prefix using wine 1.7.24.
It was necessary to fetch the full OriginSetup.exe as opposed to OriginThinSetup.exe, which is the one you'll find if you just go to the Origin website.
http://download.dm.origin.com/origin/live/OriginSetup.exe
I set it up as an XP environment. I also enabled a virtual desktop.
You then have to install the network patch to resolve download speeds under Origin. I don't tend to get more than 1MB/s, but so it goes.
https://bugs.winehq.org/show_bug.cgi?id=31438#c128
That done, you should be able to download and install any game. Each game of course might have it's own requirements.
There is also a bug whereby the C:\Program Files\Origin\EAProxyInstaller.exe never exits. The install actually completes, but the installer remains stuck. You have to kill it, after which the game becomes available. You can use the pkill command on the console to do this easily:
# pkill EAProxyInstalle
The Sims 3 does not seem to run; I found by running PlayOnLinux in a console, that the error message was
A search found this winehq bug:
https://bugs.winehq.org/show_bug.cgi?id=30988
From PlayOnLinux, choose your Origin install, and go to Configure -> Install components, and install dotnet35sp1.
This component installer runs quite a lot of things, and took a long time to install. Afterwards, however, I found the Sims 3 Launcher actually worked, and I was able to both update and run The Sims 3.
It's just the S3 Launcher that is finicky; the game itself runs well.