I doubt he's sitting in a stuck car, but it wouldn't be hard to get it stuck. The Presidential vehicle has to weigh 10,000 lbs with all the armor on it.
All of that extra weight would actually make it easier to prevent it from being stuck.
I’ve driven on ice and snow layered Colorado roads since I was 12. Folks here actually shovel snow into the beds of their pickups to increase their weight for better traction.