I was shooting this weekend with an M2 at -10C in Seoul. The M camera works well below this temperature. Most likely your wife will complain about the temperature before the camera does - from experience. The only problem is that you will need to shoot with gloves, your fingers will not last very long outdoors. This brings another problem: since you're shooting a mechanical camera, either you're very experienced, and you can meter in your brain, or you need an external meter - and you don't have the luxury of taking it out of your bag for each shot to meter. I'd say, since this is a honeymoon, bring a point and shoot (borrow, buy, etc) or perhaps a smartphone - but beware, my iPhone 4s shuts down at 60% battery level when exposed to freezing temperatures. With thick gloves I usually don't rewind the film outdoors - preferring to do it in cafes (explaining why I drink a lot of hot coffee when shooting in winter). The solution to this is, of course, a second M4!
If you still think you still want to do only film, there are plenty of shops selling film in Chungmuro (충무로). Some too in Namdaemun, but I'd argue Chungmuro is where the film people hang out. I think I have seen 400H there. I can't recall, I only shoot 400TX. PM me if you need directions, and recommendations. I think I spend too much time in Chungmuro. But 6 days, 12 rolls of 400H is more than enough. There will be some good days, and there will be some down days.
Best advice to follow is a previous post to test out the camera before using it on an important occasion. M4 is a fine camera, but you might have mechanical adjustments to make if it has been sitting on the shelf for decades, or rangefinder might be out of whack, etc.