Actually, it's not so much from it melting slowly as it it is from it melting too rapidly.  Snow melts because the exterior  roof surface is too warm (from heat leeching from the inside out).  If the roof was better insulated AND VENTED, this melting and the resulting ice damming would not occur (in most cold situations).

Read the Dept of Energy's Guide to Roof Insulation & Ventilation for Cold Climates (It's different for hot, humid climates) -
http://apps1.eere.energy.gov/buildings/publications/pdfs/building_america/26450.pdf

The melted roof snow runs down from the under-insulated roof and freezes (again) when it hits the roof edges (the eave)  because eaves (the overhangs) are uninsulated (i.e. cold/frozen). This is generally a sign of an under-insulated roof that lacks roof ventilation.  The over spill of the melted snow running down the roof results in  icicles forming on the (uninsulated) gutters.
 The water would likely not run off/overspill if the gutters were either unclogged or properly sized.  Sometimes adding to the improper insulation system are clogged or undersized gutter system which creates a scenario where the water over-flows the gutters edge-- and freezes when the temp is cold enough (i.e. resulting in icicles.)

Roof Insulation alone w/out roof venting is only a partial solution.  One needs to keep the roof surface COLD so that the snow actually sits on the roof on cold days, but melts more gradually.  This is the CORRECT PRACTICE of insulating & venting a roof in snow climates.

So the CORRECT course of action is to better insulate AND VENTILATE your roof.  The DOE website and the PDF listed herein tell you how.  You should also check that your gutters & downspouts are the proper size and are not clogged going into the winter months.  If you have ice damming (& icicles), the snow is telling you that you are wasting energy, and that you've got to better insulate & ventilate your roof

Icicles form when the warmth of the house melts the snow on the roof. Water flows down until its hits a cold area, then freezes again.

Its a warning sign of a more serious problem--ice dams, which are the frozen patches of ice on the roof itself.

You can prevent them by adequately insulating your attic, so no warm air escapes to melt the snow.

Ice forms on the gutters of your home because the snow from the roof melts slowly and builds up on the gutters, freezing as individual drops start to fall. The best way to prevent this from happening is purchase a roof/snow rake and remove the snow from your roof before it starts melting.

http://www.roofrake.com/Productpages/roofrakemenu.asp