While an ice dam can form on your roof during any snowstorm, they are most likely to form after a very heavy snowfall, when you have days or weeks of melt and refreeze cycles, or when the angle of the sun is higher, as in late winter and early spring.
During the day heat from the sun, and from your home radiating up through the roof, melts some of the snow and the water runs down under the snow to the surface of your roof.
The water from melting snow refreezes in your gutter or on the roof surface when the sun goes down and temperatures dip back below freezing. Over time the ice can build up in and block your gutter, which stays colder than your roof.
March is always a turbulent weather month. Snow one day & high temperatures in the 60s the next. The average high temperature in Lakeville on March 10th is 40 degrees F. The average low is 23 degrees.
Weather Underground reports that the record high was 77 degrees in 1977 and the record low was -5 in 1984.
The higher sun angle in late winter and early spring melts more snow on roofs than say during a January storm. So storms with a lower total snow accumulation can actually cause more ice dams.
Now you are wondering what difference it makes if you have ice on your roof. Icicles are pretty so why can't you just leave them alone?
When ice dams form under the snow (or just by themselves during an ice storm), water can't drain off your roof like it normally would.
In the images on this page you can clearly see a line of ice under the snow at the gutter. However, sometimes you can't see anything but icicles.
If you have an asphalt or slate shingle roof, the water can back up under the shingles and leak into your home. This can cause damage to walls, ceilings and hardwood floors or mold and mildew growth.
Metal roof owners do not always escape unscathed. The metal has joints and seams where water can make its way in to the interior of a building when it cannot drain off.
Raking snow from the lower 1 or 2 feet of roof will usually prevent ice from building up. That said, not everyone physically able, has the time or can convince their kids to do it. Apple Creek does not rake roofs either.
To help prevent ice dams a simple thing you can do is make sure your gutters are clear of leaves & debris and that the leader outlets are not blocked with leaves or snow. This will keep the melt water moving.
Also, many home improvement and hardware stores carry ice melting products that are safe for use on roof shingles. These can be used either as a pre-treatment to prevent ice buildup or as a way to melt a dam that has already formed.
Not every roof has shingles or gutters but they can still develop ice dams. There are many products available the purport to prevent an ice dam.
Here are links to some other information that you may find useful.
Preventing Ice Dams - This Old House
Prevent and Remove Ice Dams - Travelers Insurance
Icicles - The Farmer's Almanac