I ran my trackday mini on 10" split rims, and that handled very well, but TBH they still drive more or less the same on 12" rims providing you have the right tyres.

Ive had 10/12/13/14 inch wheels on various minis I have owned, and its only when going to 13 that you really notice a big difference.

The key thing with the 12" is to be on 165 wide tyres and to keep the profile to a 60 at most

Offset of course is also key!