This may be a dumb question but I'm an idiot so bear with me. Would the size of the tire make a difference in snow or would just the type of tire play a factor.

I went off road twice today because my tires just slid, with ABS, no traction with just a dusting on the ground. I have 20s on now, just wondering if I should put my stock tires on for the winter or buy new tires for the 20s. Thanks.