(If it doesnt matter on the temperature then why does the oil grade have xxW xx)?
This is how the oil Viscosity is indicated according to SAE system applicable & accepted almost in whole world.
(For example if its 10W 40 it actually means that 10 is the cold viscosity and 40 is the hot) !
No sir. Its not correct. Please spare time to read "Motor Oil" on wiki. And especially read the area of "multigrade oil". you will have the exact idea.
(Why do people switch to 10w 40 in winter from 20w 50 ? ! I would really appriciate if u explain how should we choose the oil)?
I know many people are doing. But this is not good practice.
Knowing few basics are easy. Like
What manufacturer has recommended in the manual. For example if its 5/30, then its suitable for all year usage. NOT to change in winter and summer.
As per other posts, every type of oil (0/30, 10/40, 20/50 etc.) produces a certain working pressure in the engine. So manual also briefs the engine's operating pressures (min. & max.) in unites 'cst'.
Min. viscosity 100C/cST Max. viscosity 100C/cST
20 5.6 9.30
30 9.3 12.5
40 12.5 16.3
50 16.3 21.9
Hence we can choose more options by ourself according to these given pressure ranges.
Source: http://www.oilspecifications.org/articles/what-is-viscosity.php