Personally I get a lot of trips where either my feet go numb while traveling through cold snow climbs or if my gloves get wet on other trips. And of course then when it warms up it becomes horribly painful. But I sometimes wonder if I get this more than most mountaineers, or perhaps I just don't have the right gear. Or perhaps I get colder hands and feet due to circulation problems? When my feet remain dry they usually don't go numb, but then again on cold days my hands manage to get either really cold or numb.

I'm usually pretty careful to keep my hands warm. Once your hands go numb, you've got real problems if you need to rope up, put on crampons, or just zip up your jacket.
But a couple weeks ago I set out for a small, easy peak. I knew the weather was cold (around ten F) and there'd be a breeze at the top (gusts to 30mph or so) but I was trying to move fast so I wore no insulation on my legs, just a softshell (which isn't windproof), and I soon stripped down to a light fleece. That was good as long as I kept chugging uphill, but I was also running a little late so I never stopped for food or water. By the time I hit the top and suddenly was exposed to the wind, I was pretty spent. Luckily I'd put on a couple layers (including my down jacket) just before hitting the top, but by then my hands had already started going numb and they didn't fully recover until a while later when I was on my way down. Pretty stupid, really.
Even stupider was what I did earlier in the season. I was looking to go ice climbing at an unfamiliar crag. I was wearing snow pants, fleece, and belay jacket, and carrying a pack with my rope, screws, etc. For some reason I wasn't wearing gloves. So I started uphill on a rough climber's trail, looking for decent ice, and of course I needed to use my hands, which meant plunging them into snow to look for handholds. After about ten minutes of this I almost passed out - from overheating. Even though my hands were painfully cold, I was wearing far too many layers for the level of exertion. After two minutes of sitting in the snow with my jacket unzipped, I was fine - though my hands were still cold.
The moral is: you need to monitor your extremities separately from your core. Letting either one get too cold or too hot can be a problem.
My feet almost never get cold, but I find I have to pay attention to my hands - they go quickly from cold to sweating, and back.

If your fingers or toes turn white, first in splotchy patches and then over a whole section of finger, when they go numb, then you likely have Raynaud's Syndrome. It's very painful as they re-warm if they've gotten seriously cold. My fingers will start turning white if I stay in the dairy aisle in the grocery store too long. You can have Raynaud's in your fingers or toes or both, or it can be worse for one or the other.

If you suspect Raynaud's, talk with your doctor about taking nifedipine (brand name Procardia). It comes in either a slow-release variety (take 30 mg) or an all-at-once release (take 10 mg). I've heard different people say they get more relief with one or the other. The slow release didn't kick in fast enough for me. The all-at-once works within 15 minutes (you can feel it) and, for me, it lasts all day even for a very long day. You only need to take it when you're going to be out in the cold, not every day. It's not fool-proof -- if you take off your mitts for too long, your hands will still get cold. But they'll re-warm much more easily.

Sadly I don't investigate my hands when they are numb because I often fear that it will make the problem worse, so perhaps one of these days I should do an inspection. I've seen my hands turn all kinds of colors, purple, blueish, pale and all the in between when getting super cold. But usually it's actually numb when I have gloves on and am in a rush to get the "motion" back in them to worry about inspecting them. It's not just the numbness that's bad, it's also when my hands become so cold they become useless. As for my feet, almost never do they get cold when dry, mostly when they are soaking wet. I suppose I ought to fix up my holey gaitors.

Raynaud's is distinctly white, corpse-like. If you take the gloves off for a very short time (couple minutes), sometimes the cold will cause the blood to rush there and will actually help. If it's Raynaud's, you'll be much happier with a very serious expedition mitt than with gloves. Keep a pair of thin warm gloves in an inside pocket to keep them warm, and slip them on instead when you need to have your fingers to do something like tie a knot. Don't wear liner gloves inside the mitts -- the point is to have skin contact between your fingers.

Ha, good post! I've been wanting to ask about this for weeks now. I seem to get hit by this pretty badly. Especially when there's wind. Last weekend I got up and tried to take down my tent, but it was almost impossible because I couldn't wear gloves to do it, but my hands would instantly go numb in the windy cold. Took me what seemed like hours to get everything in my backpack. My core was fine and I had just had a small breakfast with hot tea in my tent.