Gerard, in the balanced situation we agree that the flip risk is unaffected by tractor direction. Therefore, the risk is a break in traction that results in a side slip. Your argument for rear wheel downhill has three components: (1) the traction-affecting directionality of the tread, (2) the greater size of the downhill rear wheel, and (3) the weight that is shifted onto the downhill wheel. Let's look at each component separately.
You are on the steep snowy hill going up to the Carrier Dome. Your car is evenly weitht balanced, has all the tires the same size with non-directional tread. Your car has fwd, rwd and 4wd. To avoid sideslipping traction risks do you go up the hill in fwd or rwd. I say fwd. If traction breaks on the front drive wheels there may be some back slipping and side jigglling, but the traction will probably catch again and the front-driving wheels will pull you back up on a straight course. If you are in rwd and traction breaks on the rear wheels, you will never recover onto a straight course even if the rear wheels catch again. I think this argument holds true, even though more weight is on the downhill axle than the uphill axle. Thus I do not agree that your weitht shift component for traction-saving is valid.
What about the tread component. Well, so far we have differnt views on whether ags have more traction going forward. (I'm not saying your wrong). But if we were on turfs, you would have to concede this component, too. And even if ags have more traction going forward, how much is the differential? Does it outweith the uphill pulling benefit? What about R4's.
Your third component argument would assume you car was now outfitted with larger tires on the rear (nodirectional and evenly balanced). Do you go up in rwd over fwd? Maybe the chance of breaking traction on the larger wheel is less than on the smaller wheel, but even if so, once it breaks on the rear wheel, you will not recover and are a goner. Plus, I'm not sure that there would be any traction differece if all the tires are filled with snow or mud. Wouldnt it be better to go up the hill backwards in four wheel drive. Your big diameter wheels will be pulling up hill and your front wheels, albeit smaller, will also be driving with a weight shipt on them.
I think your arguments have force, but I still dont think the combined effects outweith the clear anti-side sliding value of driving backwards uphill in 4wd.
By the way, if you are right and we should go up frontwards, do we agree that you should have rear wheel differential lock on to minimize side slip?