How does the length of the studs on winter tires affect traction on ice? How does the length of the studs on winter tires affect traction on different surfaces?
I recently bought a pair of Nokian Hakkapeliitta W106 tires for my around-town cruiser. These studs are pretty small, as tires go; these are meant to be good all-around winter tires, not specific ice or deep-snow tires. 

The next time I go on a ride on ice or snow, I'll want to get studded tires appropriate to the conditions, probably for my 700c touring bike. (I'm hoping to find them reduced at the end of the winter season.) 


How does the length of the stud affect handling?
What kind of tires will I need for icy roads? 
Is it possible to have aggressively studded tires at the same time as full fenders (SKB plastic fenders with metal cores, in my case) or would I need to remove my fenders for the winter?
They're not really that short; compare them to the studs in studded car tires, for example.  A tiny bit of metal gives you a huge amount of traction on ice.  The real trick is that, unless you're purely riding on frozen lakebeds, you need studs small enough to deform into the tire when riding on pavement.

In icy conditions I ride 37mm Nokian W240's, they fit just fine under my 65mm Cascadia 29er fenders.  In snowy conditions, however, the snow can build up under the fender and make it difficult to ride.

If you are planning on riding long distances in deep snow there are only a small number of options, chief among which are the the Surly Endomorph or Larry tires. At 3.5" wide and at low PSI there is no comparing with a smaller tire.  Of course, you need a special bike and rims to run those beasts.