In a word: No!
There are two possibilities and it depends on how the heater and supply lights are flashing. If the lights are flashing on and off equally, that is they are on for the same amount of time then this means that the GIT-4 is doing a GFEP self test and...
No, using an external contactor will cause the GIT-4 to indicate a ground fault and keep it from functioning.
The snow sensors require a temperature below 38F and moisture on the moisture grid. The GIT-4 snow sensor has a protruding tube that contains the temperature sensor and the moisture grid is on the opposite end.
Unfortunately no, the sensor and controller of the GIT-4 communicate via a data link that cannot be simulated.