I'm a contractor in Maine and we certainly have a lot of experience with ice dams. An ice dam can be the quickest way to force water under the roof shingles even on a roof in good shape.
I have had mixed results with heat tapes. When they are used properly, they can be somewhat effective. Most folks expect to see a nice bare zig zag pattern along the edge of the roof with the ice gone around the tape. Not how it works!
If you carefully read all the directions on many of the competing brand heat tapes out there, you will see that they do not claim to remove ice dams. They are designed only to create a small open tunnel under the ice dam to allow water that is trapped above the dam to drain off the roof. This is great in theory but here is where the reality sets in. If the tape does not extend slightly beyond or below the drip edge of the roof, it won't work. If the top edge of the tape does not extend above the ice dam, they will not work. If the gutters fill with ice and bridge the ice to the roof, they won't work.
Many of the tapes instruct you to only operate them when outdoor temps are 30 degrees and above. I have found that they are ineffective in temps much below 20 degrees. They also caution not to let them run continuously.
Running them in the bottom of a gutter is almost a complete waste of time and money. Since they only are capable of melting a small area around the tape, a gutter full of ice will stay full of ice! If the downspout is blocked with ice, forget it!
What I have also found is that folks get a false sense of security when they have them installed and neglect to remove the snow from the bottom 3 to 6 feet of their roofs, figuring the tape is a substitute for roof shoveling. Obviously, when they are installed, shoveling or using a roof rake gets a little tricky, so as not to rip the tape right off the roof.
I guess you can tell I am not a fan of these heat tapes. One method I have found to be extremely effective with dealing with an ice damn are nylon stockings or pantyhose (cut into two sections) filled with salt, calcium chloride or potassium chloride placed over the dam. They last several days and melt slowly and make a nice wide valley in the ice. I have seen hundreds of gallons of water pour off from behind an ice dam using them. Chopping the ice dam can damage the shingles and can be dangerous, but the filled stockings are fairly quick and easy.
If you have plants below or are concerned about salt staining your roof or siding etc, I highly recommend Potassium Chloride which will not harm plants, grass etc. You can usually find potassium chloride at your local hardware store.
I can't take credit for discovering this method, but thankfully I learned it from a tip on This Old House many years ago. I usually make up dozens of them in advance, so I am ready for all the calls from folks who wait too long and call to see if I can come fix the water leaking through their ceilings!
Ok gentilmen , lets talk ice dams. First and foremost, what causes an ice dam to form anyway. Heat trapped in an attic, either from heat loss from the house or sun beating on the roof, cannot escape quickly and melts snow on the roof. This water drains to the bottom of the roof where it runs across a cold edge and freezes. The overhang of your roof (soffit area) is typically not over a heated area and tends to be very cold, much colder that the rest of the roof. Even with a well insulated ceiling and good ventilation ice dams will form if conditions are right. This is where the old saying,"an ounce of prevention is worth a pound of cure" rings true. Any time you have a heavy snow load on your roof followed by some moderate temps or sunny days, some natural melting is going to occur, especially if the ridge vents are buried in snow. Sun hitting the gable ends will heat up the attic a bit too. Many times the ice dam starts in the gutters then bridges over to the roof edge and starts it's way up. Once it starts, there is now way to stop it unless the source of water building it is taken away. The only way to deprive the ice dam of more water is to REMOVE THE SNOW FROM THE ROOF AND MAKE AN EXIT FOR ANY REMAINING WATER TO DRAIN. This is why it is so important to use a roof rake soon after a snowfall to remove several feet of snow from the edge of the roof. With the snow removed, you can see if a dam is starting and can address it quickly while it is small and easy to treat. Other things to consider may include, if you live in an area where your ridge vent commonly is covered in snow, add a gable end vent on both sides of the house and be sure the soffit vents are equipped with "proper vent panels" inside and that they are not blocked by insulation. Always use a minimum of 6 feet of Grace ice and water shield, or if you want a good insurance policy against leaks, cover the entire roof with Grace before shingling. This may cost a bit more up front, but pays for itself in the long run. Maximize your attic insulation. Take a good look at your gutters and consider lowering them if they are too close to the drip edge where ice dams begin. There is no one thing that will prevent ice dams, but if you look at all the preventions at your disposal, dealing with them will be a lot easier. Sorry for preaching guys, but I give this same speel to many customers every year when water is leaking in their homes and they are shelling out big bucks for repairs. Two years ago here in Maine, the huge snowfalls and subsiquint ice dam problems prompted homeowners insurance companies to send out letters telling policy holders that they would not cover a second loss if these precautions were not met.
Best Answer
Longer overhangs could impact ice dam formation, but it does not seem to be a significant factor. As this page from the University of Minnesota outlines, heat loss through the roof is the big contributing factor. They even go further and say that air leakages around light fixtures and such on the ceiling of the top story are the biggest culprits. Nowhere on that page is the size of the roof eaves even mentioned.
Longer eaves could increase the size of the ice dams, possibly preventing or delaying damage to the structure of the house. Or the water may freeze before it reaches the edge of the roof, as if the eaves were shorter. It probably depends on the temperature differential on the roof and how cold it is outside.
In any case, icicles are a sign of heat loss through the roof, and corrective action is advised. It may be as simple as adding insulation in the attic, but may involve sealing up areas around light fixtures, moving exhaust ducts (e.g., driers), using fireplaces less, etc.