First of all, let me state here and now that I am not in any way knowledgeable about the way the Nvidia drivers and Wine interact - otherwise, rather than rambling, I would look into fixing/assisting to fix this. But I am in the dark pretty much here.
Installed Wine on my machine (running Xubuntu 14.04) a week or two ago - and it forces you to uninstall something called libOpenCl or Nvidia-opencl-something or other. As soon as I spotted that Wine intended to remove a library which was related to the graphics driver, I knew it was going to be a problem. And sure enough - the machine became unstable and I had to spend many hours fixing it.
Afterwards, I spotted this article from AskUbuntu which suggests a workaround (which I am installing as I type - but it is massive and my internet sucks).
The sad thing is that this workaround - assuming it works - has been online since April 2014 - well over a year! Yet no fix has appeared in the *buntu repositories to deal with what must be a fairly regular issue (this article alone has had almost 34,000 hits!)
Quite surprised that a popular piece of software like Wine (and yes, I do note that the issue is more with the nvidia stuff than wine, but really...) isn't sorted more quickly than this!
Update: Typically, this doesn't work with my old Nvidia card - I get dumped into a low res screen and have had to revert back. Ah well. I guess I could spend hours more on this but I can't be bothered.