To find the complement of a probability, we use the formula:

$P(\text{not snowing}) = 1 - P(\text{snowing})$

Given that the probability of snowing on January 1st is $P(\text{snowing}) = 0.477$, the complement is:

$P(\text{not snowing}) = 1 - 0.477 = 0.523$

Thus, the probability that it will not snow on January 1st in a given year is $\mathbf{0.523}$.

Let me know if you want further explanation or have any questions!

Related questions:

1. What is the sum of probabilities of complementary events?
2. How do you calculate the probability of a union of two independent events?
3. What is the interpretation of a probability of 0 and 1 in this context?
4. How does the complement rule apply to more complex weather patterns?
5. If the probability of snow increases to 0.6, what would the complement be?

Tip: The complement of an event always sums with the original event's probability to equal 1.