0 would be its weight when the engine is hot, 50 would be its weight when the engine is cold. 0W50 or 5w50 would be the same weight when starting cold...???
No, in multi-grade oils, as in 0w50 or 10w30, the "w" is annotating the viscosity when its cold. The second number is the viscosity when hot, by standard that's usually at 100 deg C.
Some refer to the "w" as winter weight to signify that its a cold weight that uses modifiers if that helps keep it straight.
There is no base "0 weight" oil, there is "0w" which is two separate things. "0 weight" would imply that the oil itself without modifiers is "0 weight"; while "0w" is implying that the base stock oil of whatever weight it is, is being modified to comply with "0w" specifications known as VIIs. Think of it as honey. Its thick when you pour it, add a little water and it thins it out at room temp. Now heat it up and evap the water out of it and it thickens back up. VIIs are acting like the water in that little test. They lower the viscosity of the oil while its cold.
Same holds true to the 50 portion, it can be a standard 50 or it could be a modified 50 if they use a base stock lower then 50. They would use VIIs to thicken it say from a 30 base weight up to the viscosity of a 50 when hot (100C).
Remember viscosity changes with temp. You could run straight 50 weight oil in your quad since that's the weight of the oil when its hot right? The answer is no because the oil is so thick when cold it can't be pumped up to the top end and provide oil pressure. Once the oil is hot it would pump just like the 2w50 Polaris oil does because the heat viscosity of 50 weight is thinner then the cold viscosity of 50 weight. So you'd probably kill the top end by doing straight 50 weight, hence why we all use a 0w, 5w, 10w etc.
To my argument earlier, was about the effect of very cold oil where outside temp is below freezing. The potential to short the life of engine components is greater when using the wrong weight of oil. Very similar to the above scenario of using straight 50 weight.
As for the final weight a manufacture recommends, I would not stray too far from that at all. That number comes from oil pump pressure at operating temp, sealing ability, load carrying capacity of oil weight, "cushioning" between bearings and seals, etc.
Hope this clarifies a bit more.
EDIT: while wikipedia is not the end all be all, here's a link that gives some decent info. Look at the grade area for what we are discussing http://en.wikipedia.org/wiki/Motor_oil