Adding Attic/Roof Ventilation?

[1parkpointer]

Our house is a two-story log, with a gambrel style roof. The second floor roof walls are actually trusses, which give flat 2nd floor ceilings and vertical walls with no knee wall; and the second floor end walls are conventional 2x6 construction.
The 2nd floor roof wall has a soffit vent at its base, which runs the entire length on each side of the house. Proper Vent is attached in between each truss and starts just above the soffit then runs vertically up the roof to the (gambrel) pitch change and then continues on between the top roof trusses for another 5 to 6 feet. The roof has a ridge vent along its entire length.
We live in Central New Hampshire, so we experience cold and snowy winter seasons.
Our problem is that the attic is not as cool inside as the outside air temp. During the daylight hours, the sun warms the roof and the snow melts. The resultant water collects along the pitch change of the roof, and a portion refreezes, some drips over the edge and refreezes, basically creating a dam effect along the top edge and then along the most vertical part of the gambrel sections in various layers of freezing and refreezing. We have (3) roof windows on the more vertical section of the roof. Each roof window also collects a portion of the dripping snow melt and then the water refreezes onto the roof window. During the daytime, and for many days after each snow storm the melting continues. I'll have to put up a ladder onto the roof wall portions, and gently break off the ice.
My question is, basically after each storm, the ridge vent gets covered up with snow and stops functioning until enough snow melts to expose the shingled style ridge vent.
Should I add gable end vents to help ventilate the attic/roof and lower the inside temp to help prevent the warmer attic/roof?

[canoebuilder]

Your problem may not be 100% lack of ventilation but also loss of heat due to a bad insulating job (which also can block the ends of the proper vent.
Here in the North-East (Live in Western Maine)I always put in no less then 12 inches in ceilings. Not an option in your case for the wall section.
Also have been in attics where the insulation was jamed into the sofit so far it blocked off the proper vent. These sky-light windows are always a great heat loss area too.
If you have checked all this out and is OK then the gable end vents will be the next step to try to solve the problem but to tell the truth the way you describe the melting I think it is more a heat loss problem. I have used ridge vents on several houses built and no Ice Dam problems but I have never built a gambrel style roof either so....
Gerry