Bingo. The batteries are the issue. The electronics will actually have less noise in the cold (but technically only until you freeze out charge carriers in the semiconductors and the camera stops working altogether, but that happens below the temperatures you could survive). If you just keep two sets of batteries like spraynpray suggested, then each time the one in your camera goes "dead" (not really—just gets cold), you can swap out for warm batteries in your pocket.
Also, different batteries based on different chemical reactions will have different behaviors in the cold.
It's chemistry, if you're interested in the details. The chemical reaction in the battery that releases the electrical energy has what's called an activation barrier, which means that it needs some energy input to start the reaction but once it gets going it gives off more energy than it initially took in. It gets that energy investment from heat that it absorbs from the environment, so in a cold environment the reaction rate is a lot lower and the battery looks like it's dead. Once it warms up, the reaction rate goes up again and the battery appears to resurrect.
Most batteries now are lithium anyway, which is pretty reactive, but yeah, that's the general gist. I never thought of batteries in that sense, but it makes perfect sense.
Ah, activation barriers, I remember that from general chemistry and biochemistry... such warm memories. :D
I took my Nikon Coolpix E3700 up to Quebec City once in 2008, the 400th anniversary of it's founding in February. I don't remember specifics, but the average low for that time is -16 C, or 3 F. The average temp is -11 C, or 12 F, and I still got about 200 or so shots per battery, and since I carried 2, I was pretty much good for the day if I didn't use flash too often. And since we were out almost all day, I went out at night too, we went to the Winter Carnival for the fireworks at night, so it got pretty darn cold. Interestingly enough, all I needed was a thin pair of gloves, so it didn't really get all too incredibly cold, but it was certainly more cold than I have ever experienced.
Just Monday I took my D40 with the 35mm 1.8 out in the snow, it was right after the big blizzard in NYC. Near freezing temperatures, the camera performed like a champ. Just to be safe though, I took it out with the 35mm 1.8, it's got better sealing than the 18-135. It must have been around freezing if not below on that day. To be fair though, I went out around midday. Strangely enough, there was no condensation when I moved from indoors to outdoors, and vice versa, which I thought was odd.