From Mobil "Most oils on the shelves today are "Multigrades", which simply means that the oil falls into two viscosity grades (i.e. 10W-40 etc). In a 10W-40 for example the 10W bit (W = winter) simply means that the oil must have a certain maximum viscosity or flow at low temperature. The lower the "W" number the better the oil's cold temperature performance."
i.e. 5W/30 will flow better in extreme cold conditions but unless you are riding in -10C or more I would keep to the standard 10W/40, which Suzuki states as being suitable for -20 degree conditions. Just ride gently until the bike is warmed up.
By the chart I see that I can use 20w-50 in Phoenix AZ. I have some of that left over from dirt bikes. Some people worry too much about oil. I once bought a full case of Honda synthetic oil for a good price from someone who sold his Honda and bought some yamaha oil for his new Yamaha. I had to bite my tongue while completing the transaction.