My gut feeling tells me there can't be any considerable difference in the cold weather handling of these two cameras.
The battery in D3200 is the same EN-EL14 that was already in D3100, released in August 2010. Nikon D3300 uses a new version of this battery, EN-EL14a, which otherwise is the same but has slightly higher capacity. This has been achieved with lowering the voltage by two tenths (7,4V to 7,2V) and higher storing power (1030 mAh to 1230 mAh) resulting in total output power increase from 7,7 Wh to 8,9 Wh. These numbers do make a difference, but are not a deal breaker when talking about photographing in cold. The battery runs out of juice anyway, it is only a question if this happens a little bit sooner or later.
Other than the slightly higher capacity battery, there is nothing that I can see in these cameras that would suggest any difference in handling in cold. In the question you asked for experience in these cameras, which I have none, but I have some experience in photographing in cold. Finland is at the same latitude as Alaska.