Answer: No, it is not a statistical question
Why not? Because your best friend has a single favorite color, or perhaps a top 5, or something along those lines. Assuming that your friend doesn't change their mind, then those favorites are locked in place with no variability.
A statistical question on the other hand must have variability in the answers. If you asked a classroom of students "what is your favorite color?" then you should expect a wide variety of answers, and hence some variability is present.