The models (e.g. BSIM, EKV) are ok down to lower voltages than the threshold. I have the models for a 65nm process accurate down to 0.3V. Of course, the newer the process, the less accurate. The models get better as the vendor does more runs and records the variation distributions. The best you can do is run all combinations of global and local variations (e.g. temp, global process corners, and local variation). However, if you want what I call "research robust", then I think running global process corners (FF,FS,SF,TT,SS) and Monte-Carlo at each of these corners should be enough. If you are building a real product, then of course you need to also include temperature, which makes the simulations much more time consuming.
Good luck,
analogLow