That sounds right for water, but definitely not true for snow. I don't run when it's deep on the ground, but even a little can splash onto the uppers and then soak through. It's like running through shallow puddles half the time, not fording a stream. I know from experience - maybe a thousand miles of running in New England winters over the last few years - that Gore Tex and similar barrier fabrics avoid that problem quite well.

Those same shoes usually come with high-traction soles (both materials and tread pattern) which are also essential in those conditions. And of course they're warmer. Winter running in summer shoes would be a recipe for freezing, blisters, or injury around here.