Yes. And you can still find them. Some makers called them 'Mud' tires. Colloquially they are called 'knobbies'. They generally were over-sized. And yes, tire chains were (and still are) available for the Model A tire size.
Let's not forget the walnut shell tires from the 30's through the 60's, Soft rubber tread impregnated with ground up walnut shells - they were great traction on snow and ice! I told my son about them once but, like his generation, I don't think he believed me. He still refuses to believe that a Snickers bar cost a nickel and a Baby Ruth was 2 cents.
mjw, post #8 :
The Universal tread pattern on your 16 tires is the same as the original 19" Ford-issued GoodYear tires, and the same pattern that is used on the current production of the GoodYear 19" & 21" Model A tires. Not particularly aggressive or 'mud/snow worthy', but an exciting and authentically original tread pattern.