Problems with Edge 510 Cadence/Speed Sensor
I also have an Edge 510 (since ~3 months) with the same sensor, but I have not experienced this. I have recently updated to the latest firmware, which often solves similar issues with power readings.

Since you were riding at quite low temperatures, the capacity of the battery does decrease, but since the speed reading is fine I would not suspect the battery if the sensor/battery is not old (?).

There is a line/groove on both the sensor and the magnet -- check that they still line up properly. 

Check also that the sensor is installed in the correct orientation: the battery cover faces the wheel in my case. 

You should also verify if the sensor also acts this way when used indoors at room temperature.