How to prepare oneself for riding in the snow?
Studded tires are a must on ice. They are expensive, but well worth it! A couple of points to consider that have not been mentioned:

Footwear: Winter specific riding shoes or boots. For mountain biking and cross, I ride with Lake boots. On the road, I use an older pair of road shoes that have been stretched to accommodate thick wool socks and neoprene shoe covers.

Head-wear: I typically ride with a helmet cover all winter. I also bring along a couple different varieties of skull caps on ride ranging in thickness, ear/face coverage etc... yes to balaclavas!!!

Depth of snow: whether you are running studs or not, my experience is that if the snow is deeper than 4-5 inches, it is not ride-able. In this case, it is best to wait until either the cross country skiers, hikers or plows(in the case of roads) have cleared or packed down the snow.  

Body Temperature: Many cyclists new to riding in colder weather tend to over dress. The trick that works for me is twofold, first absolutely dress in layers and second I want to be cold, not freezing, but cold as I go outside and get my bike ready or at the very start of the ride. If I am warm at that point, I will be sweat soaked in the matter of minutes and wetness is something you want avoid! 

Fender: Clearly, if the snow is dry, it is not necessary, but my experience is it is better to have one as a precaution than go without! 

Heat Packs: At extreme temperatures, I have successfully used heat packs in the tips of my shoes and palms of my gloves. I am not a huge fan of use in the palms, I very rarely and if i do it is usually just a temporary fix.

Use of Car Heater: If I am driving to the ride, I preheat my shoes and as much clothing as possible using my car heater on the way to the ride.

If you get yourself set up with studs, I would highly recommend finding a frozen lake or pond to ride on! The experience is phenomenal! If you can time the lake ride with 1-2 inches of fresh snow it will be that much better!

I ride road, mountain and cross year round outside. Hope this helps!