Not directly. The mass of the wind is so low that it has little dynamical effect upon them, especially in low earth orbit. The problem is that when the wind is high during a solar storm, it compresses the Earth's magnetosphere and can cause energetic particles to be accelerated during what are called magnetic re-connection events. These particles can produce secondary radiation in the spacecraft skin which leads to enhanced radiation dosage. Usually, however, the effect is small enough that the proximity of the astronauts to the inner Van Allen radiation belt is a far more significant problem.
All answers are provided by Dr. Sten Odenwald (Raytheon STX)
NASA IMAGE/POETRY Education and Public Outreach program.