It may not be totally obvious that this is a picture of a frozen downspout.  It’s solid from one end to the other.  The tell tail sign of problems seems to be dirty icicles forming on the siding.  This indicates that the water has already entered the exterior and exited.  It’s what is not exiting that we are worried about.

The questions is what to do about it?  It seems like the first course of action is to disconnect the downspouts at the gutter so that water is being directed away from the house.  We’re clearing as much snow as we can off the edge of the roof (there is no safe way to access the rest of it).  You can try putting de-icer in the gutters as well.  Whether or not it will help is questionable but it probably can’t hurt.

Here’s a good link for more information on ice dams.  It’s worth noting that three of the four houses I know of currently suffering from the problem in Portland are pre-1910.  The other is new construction.  The new construction does not have the icicles on the siding- their water is draining directly into the house around the chimney (which is probably melting the snow and ice around it.