No.
You can often see urine or peeing on a chilblain advised. However, there is no evidence that urine therapy works and there is no rationale for doing it. There is nothing in urine that can affect the physiological processes of chilblains.
Urine therapy is widely recommended for everything from cancer to cuts on the skin, but there is absolutely no evidence that it works for anything or anyone, yet you can come across so many anecdotes and testimonials online that urine has great healing powers (it doesn’t). If urine therapy appears to help anyone, then it more likely helps as its a placebo or the condition was going to get better anyway.
What is in the urine is there for two reasons: One, it is surplus to the body’s needs, so the body excretes it; and, two, its toxic or harmful to the body, so the body excretes it. So, why would drinking urine or applying urine to the body be useful for anything, let alone chilblains, if the contents of the urine is what the body naturally does not want?
There is a suggestion that urine treatment for chilblains may help as urine is warm and as a chilblain is a non-freezing cold injury, then the warmth of the urine may be of some use. However, there are plenty of other ways to apply warmth to a chilblain rather than rely on the non-existent magical properties of urine.