White patches mean that the wax has worn off. The longer that you leave it the dryer the base can get and the more permanent damage that can be done to it. Once they get drying damage they can lose the ability to hold wax at all.
So wax straight away. How often you should wax depends on a number of things. But the most important one is that hard snow and ice scrape it away very quickly, whereas on powder it can last for a long time.
You may also have to re-wax if you experience big changes in temperature as there are different waxes for different temps. But generally an all-temp wax will do just fine.