Date: 202101
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Small Aircraft
Operator: FBO
Operating under: Part 91
Flight plan: VFR
Mission: Training
Flight phase: Landing
Airspace: Class G ZZZ
ATC / advisory: CTAF ZZZ
Reporter organization: Contracted Service
Reporter function: Instructor; Pilot Not Flying
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Instrument
Human factors: Training / Qualification; Situational Awareness
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Ground Event / Encounter FOD; Ground Event / Encounter Weather / Turbulence
Contributing factors: Airport; Weather
Primary problem: Airport

Narrative: Aircraft X came to an abrupt stop on Runway XX at ZZZ due to snow on the runway. We were the only occupants of the craft. Neither of us were injured; nor was the plane damage. There was no damage to any other persons or property.A low approach was made to assess the condition of the runway before attempting a soft field approach and landing. We decided to make an approach to land after judging that the snow looked to be at or less than 2 inches. It looks like two layers of very thin snow. We could see tracks from another tricycle gear airplane. What we didn't realize was that that plane had landed in much shallower snow and that it had then snowed more on top. Being able to see grass protruding through the snow also gave the notion that the snow was not deep. I briefed my student on precautions to take with landing on snow before we made the approach.When we landed; the plane's mains and nose wheel sunk in causing us to come to an abrupt halt. We were able to taxi the aircraft most of the way up the runway. We agreed to attempt a soft field take off back down our tracks; which didn't get very far.Chief; Assistant Chief; Owner; and Lead Pilot were notified. We contacted the Airport Manager; who was able to come to our aid with a backhoe. We took off from the county road next to the runway as decided between myself; the Student and Chief Pilot; and as advised by the Airport Manager. A successful short field takeoff and climb out was performed by myself; the instructor and my student and I returned to ZZZ1.14 CFR 91.103; Pre-flight preparation; was not observed or fulfilled to its fullest. I will not get into the possible reasoning behind this; aside from that we decided to go to #X# during taxi.Lessons learned are abundant by our main takeaways that [we] I discussed were as follows:-New or unfamiliar airports need better preparation and scrutiny.-Snow depth should not be judged from the air. Until properly equipped and properly trained; no approach and landing should be made to a snowy runway that one is not sure they could take off from again.-I now have a new example of things not to do to use as a teaching tool with my students.We were extremely lucky pilots today. but we as pilots do not want to rely on luck. Lessons learned.




Synopsis: Small aircraft instructor pilot reports landing on contaminated runway of unknown snow depth resulted in abrupt stop and being stuck.