I go through 3 different types of shoes as the seasons change: Hot (80F+): sandals Variable (30-80F):
indoor soccer shoes (eg adidas sambas) Cold (30F-): light hiking boots/trail running shoes For cold weather, you not only need to be comfortable while pedaling on your bike, but also confident off your bike.
Lightweight hiking boots, with windproofing, waterproofing, and breathable layers, not only keep your feet happy while pealing but also let you feel like a mountain goat when you put your foot down in the slush at a stop light, or dismount on top of ice, or have to portage down wet stairs.
Trail running shoes with these attributes are also a great choice if you want something even lighter and without the additional ankle support.
As others mention, wool/smartwool socks and switching to platform/toe clip/half-clips on your pedals are both good changes in addition to changing up your footwear.
My winter setup is smartwool socks, size 13 light hiking boots from North Face and Velo Orange half-clips.
bicycles.stackexchange.com/users/735/Noel
In the winter I wear neoprene overshoes/galoshes.
(Some kind of socks on the outside of my shoes): These are not intended for walking.
They wear very much, and the nose slides up, even after a few steps.
The bottom is open, so you can use your SPD or other clickless pedals.
But while cycling they keep your foot dry and warm.
And they protect your shoes from dirt and mud.
In the autumn and winter, I always wear them for "sport cycling" (mtb, road).
I wished they were around when used to cycle to school (20 km through open terrain).
bicycles.stackexchange.com/users/444/GvS
I haven't tried it myself, but according to the quite informative ICEBIKE website , sandals with layers of socks, including breathable waterproof ones, works quite well.
There are a number of cyclists, not always in the coldest of climates, but plenty chilly never the less, that swear by SPD Sandals, either from Shimano, or those pictured at right from Lake.
What's this, you say, are they Daft?
Not at all.
Sandals adopt quickly to the addition of another layer of socks, Gore-Tex Oversocks, or neoprene booties.
When out in the cold wet, you won't have wet shoes, as no water accumulates, it all runs off.
Personally, I just wear boots, and use toe clips or bare platforms depending on the size of the boots.
bicycles.stackexchange.com/users/454/Brian Campbell
I have done the sandals and socks through the winter, living in Minnesota.
I usually would wear 3 layers of wool socks.
When it was wet, I'd put a plastic bag between the outermost sock and the next one in.
It worked very well and my feet were never cold.
There are companies that make specialized products for the socks with sandals in the wintertime though.
You sure do look kinda funny when you do that though.
bicycles.stackexchange.com/users/683/whatsisname
I've got some "toe warmer" type things that slip over the front of my cycling shoes.
Has an opening in them to go around the clipping mechanism.
Works surprisingly well.
I go cycling in the snow with them, but have not gone out in days colder than upper 20's (F).
bicycles.stackexchange.com/users/349/Brian Knoblauch
Living here in Southern California doesn't make me the best judge of "wet and cold" cycling gear, but I have had a few experiences in heavy downpours.
Being low on a budget, I find that it's often easy enough to slip a plastic bag over my socks and then lacing up my shoes, but there is a serious lack of style there, not to mention that your feet can't breath.
I have found a better alternative to keeping my feet dry regardless of what shoes I happen to wear, but it requires a little bit of work.
I happen to be lucky enough to own one of those wooden shoe inserts that help retain the shoes' shape.
Anyhow, through layering plastic bags and ironing them together, I was able to make a thicker "fabric" of sorts which was molded to the shape of the inside of my shoe.
I also made some that fit over the shoe, and it has done an incredibly good job at keeping my feet dry, on a low budget, with minimal weight increase.
Another solution which works quite well are neoprene socks which you can wear directly over your feet, or over a few layers of socks.
While they are a little pricey, it helps your feet breath and keeps the cold water out.
And while I have not tried it myself, I hear that shoe covers work just as nicely.
There are many winter foot wear options
so I thought I'd list a few.
bicycles.stackexchange.com/users/781/Teddy 
I've been using Lake's winter biking shoe for many years.
The latest model (MXZ302) is absolutely superb.
They fixed the main problem the shoe had which was the escape of heat through the cleat.
Now with the latest MXZ302, two inner wool sock layers, and an external booty (of any brand)
I can ride in temps down to -15 (minus fifteen) celsius
(I think that's about 5 degrees farenheit) without frozen toes.
And I have chronic low blood pressure which causes my feet and fingers to go numb easily.
Now, if I could only fix the frozen finger issue...
bicycles.stackexchange.com/users/2510/John Fitzpatrick
In the winter I use Shimano MT60 MTB shoes - really comfy, gore-tex, warm and you can run cross-country in them with a bike on your shoulder.
They were fine down to -20 Centigrade last winter.
bicycles.stackexchange.com/users/2077/Rory Alsop
I used Shimano cycling sandals during the summer months here in the Chicago, Illinois area.  I'm wondering if I can use these during the cold winter months also or if different shoes are required.  In favor of continuing to use the sandals, I could add SealSkinz and/or wool sock layers as the sandals are expandable.  Other than looking strange in the winter, are there problems with doing this?  What other winter cycling footwear should be considered?
Sandals in the winter? Other winter footwear options?
bicycles.stackexchange.com
<clothes><winter><shoes>
bicycles.stackexchange.com/questions/2014
bicycles.stackexchange.com/users/718/Tim Butterfield
Suitable footwear for cycling in winter is quite varied. Ordinary boots with toe clips or bare platforms depending on the size of the boots are good. Lightweight hiking boots, winter biking shoes, Shimano shoes, trail running shoes are all possible solutions. If you wish to wear sandals, pair them with wool socks and clips on the pedals.  Another option is to cover the entire shoe with neoprene socks. However, there are companies that make specialized products for the socks with sandals in the wintertime. A good solution would be to wear boots, ideally windproof, waterproof, and breathable. You could customize them with toe clips or bare platforms. You could wear a number of biking shoes, such as Lake's and the Shimano MT60 MTB, or running shoes if you prefer a lighter construction. Moreover, you could use alternative methods to keep your feet dry and warm, such as toe warmers and handmade constructions out of plastic bags and wooden soles. Finally, specialized options for sandals include wool, smartwool and neoprene socks, and using platform or clips for warmth and insulation purposes.
A good solution would be to wear boots, ideally windproof, waterproof, and breathable. You could customize them with toe clips or bare platforms. There are a number of biking shoes available, such as Lake's cycling shoes, or the Shimano MT60 MTB shoes. You could use running shoes if you prefer a lighter construction. Specialized options for sandals include wool, smartwool and neoprene socks, and using platform or clips for warmth and insulation purposes. You could use alternative methods to keep your feet dry and warm, such as toe warmers and handmade constructions out of plastic bags and wooden soles.