In fact, it does -- to demonstrate, assume otherwise and use the definition of continuity.
> "there is no nonvanishing continuous tangent vector field on even dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0"
Which means they can all blow in a continuous path except for at least one point, so the wind at every point but 2 could be blowing east on a sphere.