Detecting when the thermostat turns on the refrigerator
Since you're monitoring a DC powered system the solution should be quite simple. Monitor the voltage to the fridge and the current consumed by it. Take a reading periodically (1s, 10s, 60s, or whatever you like) and calculate the instantaneous power (*P = V × I) and total it. If you monitor every 10 s, for example, then you can assume constant power for that interval and the energy used can be calculated by \$ E = \frac 1 {10} VI \ \text {Ws}\$. (That's watt-seconds.) To convert to watt-hours divide by 3600 (60 × 60).
You can monitor the voltage as you suggest using a voltage divider. 4:1 gives you a maximum input of 20 V which keeps your 5 V ADC input safe in the event of a spike from the alternator.
For monitoring the current you can use one of the popular ACS712 Current Sensor Modules.

Figure 1. ACS712 modules feature a simple +5 V, GND and analog output. These seem to be available in 5 A and 20 A versions. The current sense terminals are isolated from the 5 V side (see the traces on the photo) so you can monitor either the positive or negative lead to the fridge.
The module can be powered from the Arduino. Only one is needed as they have six or eight analog inputs.