I've had to have the tow truck come out twice now in my career and it was not considered an accident. It is only an accident around here if you damage the truck or someone's property.
If it has already snowed a couple of inches when you are starting your day, chain up before you leave the building. If you have miles to drive on a level highway, chain up when you get to the mountains. Just remember, deep snow, and the chains are not much help when only on one tire of a dual-wheeled truck. They will dig a hole under themselves and leave you spinning on the inside dually. Also, just because you can make the truck move, doesn't guarantee it will stop or steer. Take it slow, and anything too steep, EC.
Welcome to Brown. Not the cushy job the world thinks it is.