I've not encountered problems with E mount lenses in the winter. They are no more prone to problems than any other AF lenses I've had, and I've had quite a few.
I regularly take advantage of the peak of the winter when it gets below -20C and the sea is about to freeze, but is still open and there is sea smoke. In this environment after about one hour of use in my experience the camera fails to control the aperture of E lenses. G, D, etc. lenses have not exhibited this phenomena in my use (except one 70-200/2.8 original copy which got some dirt in the aperture mechanism, and operated wide open on two occasions, easily cleaned). With E lenses the camera can either lock up per se, or keep operating but fail to control the aperture after prolonged exposure to these conditions, depending on the camera model. This has happened with several camera bodies, including D700, D800, D810. I think the problem is the water vapour freezes on the contacts, but it could be something about the aperture mechanism itself. I initially thoght it was the weather sealing of the body itself but after I've accumulated a lot of E lenses it became clear that the problem seems to be related to them. Offending lenses include the 24, 45, 85 PC-E Nikkors and the 70-200/2.8E. The regularity of this happening is very high given sufficient exposure to open water and cold, humid air. I've tried taking out the battery and put it back in, it doesn't seem to help but mounting/unmounting the lens does allow shooting to continue, even if for a brief time. Anyway, I often shoot in the same environment with a friend who uses Canon 5D series cameras and also tilt/shift lenses and he doesn't have any problems. Canon has longer experience with electromagnetic apertures for sure. I'm not saying Canons don't have problems in the cold - some do.
Personally I do not value E Nikkors over G or earlier Nikkors specifically and don't think the new system is as reliable as the old, in the conditions that I do my winter landscape photography in. I am aware that dust and dirt can jam a G lens and am not saying it is perfect but it doesn't exibit this particular issue in my experience.
I'm not trying to discourage anyone from buying E lenses just that they're not a panacea to all problems, in their current state, and I certainly won't avoid G or other lenses because they're not "E" (I do not avoid E lenses either, if the lens has features and quality I may buy it, just that it is regrettable there appears to be this issue). My experience simply does not merit such discrimination. Without doubt the reproducibity of exposure in high fps shooting is improved in normal shooting conditions (i.e. normal temperature and humidity), and the fps rate itself can increase a bit due to the use of an E lens.
Nikon, of course do not claim that the cameras work in the conditions that I'm talking about. They specify 0 to 40C and also put limits on RH. However, for my landscape photography those rather harsh winter conditions are essential to get the effects that I want and I do want to use tilt a lot to make even sharpness in near-to-far compositions. For quick snaps, I am sure the E holds up for most users, but I could be on one spot for 15 min, 30min or longer and a few hours in one area. Unfortunately with the hard part of the winter getting shorter, it is essential that I make the best of what remains available and gear malfunction is rather annoying as it can mean the best shot of the year is missed. Yes, even in landscape photography time can be short. For now, taking off the lens and putting it back on seems to rectify the issue now that I know about it, but I have used this trick only a few times so far and I don't know if it will always work. My suspicion is on the electrical contacts being too exposed in the F mount. In Canons the lens contacts point inwards, towards the camera body. I don't know if this is the difference or if there is something else.
I have to say that this has never occurred on the large bodies (D3, D3X, D5) but I think that's just that I use the more compact bodies most of the time for landscape photography and although the large cameras are well built, I'm not terribly keen on holding them on water for a longer time. They can supply power in the cold for a longer time but again this doesn't seem to be all about that. Of course, it could be a combination of factors: power drop in combination with condensation & freezing both of the contacts and the aperture itself (maybe) instead of just one factor. It may be that the motor that controls the aperture in the body when using a G lens is better shielded from cold and condensation.