When should I worry about icicles on my gutters?
The icicles are caused by heat escaping from your house, into the attic. This melts the snow on your roof causing icicles. It has nothing to do with your gutters. 

If you want to reduce or eliminate the icicles, the best thing you can do is add insulation to your attic and seal other means of air escaping (non-sealed recessed lights leak a lot of air).

If you would rather just tackle the ice dams then you might want to consider electric heating wires on the roof which will melt the ice and prevent it from freezing on the roof and gutters.