Keeping one battery warm while you use the other should, in theory, give you better results. The battery well inside the camera is usually slightly better insulated than most grips and is also closer to the heat producing parts of the camera. Your hand wrapped around the battery well (as most cameras are designed) would provide additional insulation. The benefits are probably pretty marginal, though, compared to running a single battery in the grip while warming the other or, even better, warming two spare batteries while two batteries are in the grip.
Ditching the grip should probably be balanced with other environmental considerations. Extremely cold environments also tend to present other issues that make us not want to open up our cameras when shooting in them. Snow, ice, wind blown dust and other particles, etc. are better left outside the camera's body. If you can expect to get away with not having to open your camera at all by using two batteries in the grip that might be a better option than using a single battery in the camera (without a grip) and having to expose the interior of your camera to the environmental conditions in which you are shooting. Even if one is going to have to make several changes over the course of a session some of us would prefer to risk only the interior of our grip rather than the interior of our (presumably) much more expensive camera body. Of course this assumes that the camera/grip combination we are using is adequately weather sealed at the interface between the grip and the camera's battery well.
Another minor benefit would be the availability of the vertical controls a grip provides. When we are all bundled up, using the camera in portrait orientation without a grip is even more difficult than it is when we are wearing only a t-shirt over our upper body.