There's a lot of difference in the weight transfer under hard braking on dry roads versus lighter brake applications on snow-covered roads. Brakes generally are biased towards the front because that's where the weight transfers during hard braking (just as you described). In the old days, a proportioning valve or dissimilar master cylinder sizes (for front and rear) made a specific bias to the front. It might be a compromise of sorts, but 75% of our driving is on good traction surfaces and that's where you want your best braking.
One of the phenomenon I experienced in the past - in the winter, it was common for us to add weight to the back of our 2WD pickup trucks for traction. Coupled with a limited slip differential and real snow tires, we got great traction in those trucks. But they became rear-heavy. On slick surfaces, it was easy to lock the front brakes while the rear wheels still rolled along. And with locked front brakes, of course, comes complete loss of steering control. It was not uncommon to hit the e-brake a bit to bring the rear tires into play when stopping.
Fun times. Of course, this was before anti-lock technology became common on anything outside of the most expensive sedans. There is a lot more at play in today's cars, thanks to technology. And it's for the better.
What you describe with putting weight in the back runs on "the same," proinciple I was trying to describe before. Putting half a ton of sand or bricks in the bed gives the back better traction, and maybe even keeping better traction in hard braking. Under that circumstance, the fronts, having less traction, will skid before the rear -- all else being equal, or braking system designed for "normal" F/R weight distribution.
It's possible to stop with rear brakes only, but stopping distance would be awful compared with front-only, and all due to the force distribution involved in the dynamics of braking.