I can only speak about Prius. I know nothing about the Hondas or other hibrids. I am in Texas, so we seldom get below 20 degrees or so.
The engine runs longer on initial startup in cold weather, and it runs a bit richer than normal, the objective being to heat up the catalyst quickly. Once the engine gets up to temp, the engine will shut off at a stop, but, if you have the heater on, it will restart shortly. There is a slight drop in the overall MPG in cold wx, say maybe it drops from 47 to 45 MPG. (It's difficult to measure MPG accurately because the fuel tank bladder holds less when cold, and is difficult to top off exactly the same at each fillup).
The main thing that Prius owners up north complain about in the winter season is that the original Goodyear tires are terrible in the snow. Here we didn't have much snow last winter, so I did not have any tire complaints. This year, I may take it up north over the holidays, so I may get a better feel for overall cold weather operation.
If you really want to study up on it, I suggest Priuschat.com forums, although I haven't been there in a long time. (Too many screwball enviro whiners on there to suit me).
Few, if any actual car enthusiasts on there.