Falcon 900 Captain reported a loss of directional control and runway excursion related to loss of nose wheel steering and brakes. Reporter stated it was a very smooth landing that may have resulted in a squat switch malfunction.

Narrative

Smooth approach; very very smooth greaser landing on center line. Slight right crosswind of maximum 6 knots. On rollout; thrust reverser deployed normally but had no brakes and no nose wheel steering. Due to slight right crosswind; aircraft slowly began to weather vane to right and aircraft slowly departed runway center line at very slight angle to right and eventually off the right side of runway into foot deep thick snow which brought aircraft gradually to stop.No abnormalities observed in cockpit. Hydraulic systems all normal. No damage observed to exterior of aircraft. Was beautiful sunny day; dry runway; very light winds at ground level. Smooth approach; very very smooth greaser landing well within touchdown zone on center line. No observable abnormalities on cockpit instruments. Suspect greaser landing contributed to minimal strut compression and resultant failure of one or more proximity switches to signal that aircraft was on the ground thus disabling both normal braking AND nose wheel steering. If Maintenance inspection finds no discrepancies; this speculation might be all we end up with.