One of the decisions Nikon made when Autofocus first became a viable technology on a consumer scale about 25 years ago was to create a system that allowed it to be backwards compatible with the existing Nikon F-mount lens lineup. This meant maintaining a mechanical link between the camera body and lens to stop down to the aperture setting selected on the lens' aperture ring at the instant just before the shutter opens.

Since metering and focusing (manual or automatic) are typically done with the lens at its maximum aperture, the amount of time needed to actuate the aperture directly impacts the amount of shutter lag the camera displays. In very cold environments mechanical devices machined to tight tolerances can encounter substantially more friction than in warmer environments, especially if lubricants which begin to stiffen at certain temperatures are used.

Since you haven't indicated a specific lens in your question, I'll have to make an assumption: That you are using a D-type lens with an aperture ring on the lens. Even when the aperture is locked to the narrowest setting (usually denoted in orange) and controlled by the camera rather than the aperture ring, the mechanical linkage between the camera and lens will hold the aperture fully open until the shutter button is pressed. Then the link will move to allow the lens to stop down to the selected aperture an instant before the shutter begins to open.

On can observe the closed aperture varying slightly in shape, probably due to "bounce" of the mechanical levers connecting the lens to the camera body, as the sensor is progressively exposed in this super slow-motion video of a Nikon D3 with an AF Nikkor 50mm f/1.4D set to f/16 and 1/4000 second cycling at 11 fps.

(screenshot from video)

I suspect what has happened is that the cold environment inhibited the movement of the aperture control linkage just enough that it had not completed its movement to f/7.1 when the shutter opened for some or all of the exposures in question. The camera should have enough time to complete this movement prior to the shutter actuation when the camera is in an environment within the bounds of the manufacturers rated operating environment. The minimum rated operating temperature for the D7100 is 0ºC/32ºF. The differences from one frame to the next in terms of exposure indicate differences in the amount of time the camera needed to set the aperture at f/7.1 via the mechanical link when operating in a cooler environment.