I understand what you mean! :)
How I would go about saying them would be as follows;
1: "The soles of my shoes don't have a good grip, and the floor is slippery, so I fell down."
2: "My tires don't have good traction on snow."
Traction is the act of pulling something over a surface, so it's another way of saying "grip on a road".
I hope I helped!