The M20J has a wing area of about 175 sq ft. (actually a little less because this area includes the area under the fuselage, but this is close enough for this analysis). The weight of snow varies with water content, but lets consider wet snow which is about 20 lb per cubic foot. So, a foot of wet snow will put a downward force on the wings of 175*20 = 3250 lb. The negative load limit is -1.5g, but this is really a factor of 2.5 since there is normally +1g acting on the wings in flight. So the wings can withstand a downward force of 2.5*2900(gross weight) = 7250 lb.
The horizontal stabilizer has an area of 21.5 square feet, so a foot of wet snow will create a downward force of 430 lb. So, what will probably happen is that the airplane will end up sitting on the tail tie down. When I used to fly to Truckee CA for a day of skiing I would often see all the tied down airplanes sitting on their tails.