Anna,
Dexter, of Niflmir. I can only speculate. I'm not very strong when it comes to particle physics...I think if there was no change in the field strength only the orientation, that there wouldn't be much of an effect, except perhaps where the cosmogenic isotopes are entering the atmosphere? The isotopes I'm referring to are part of the solar wind interaction, electrons and protons (galactic cosmic rays, GCR) bombarding the planet. They form isotopes of carbon, berylium and chlorine, but those effects on the climate are at the very edge of detection.
Lots of noise is made about GCR and whatnot, but the evidence is very poor. The hypothesis is that in times of low GCR, that fewer clouds are seeded and so more incoming solar radiation reaches the surface of the earth. The problem is the time lag they've found between the GCR, and the fact that they are scavenged by other cloud forming particles. The difference between high and low cloud nucleation as a result of GCR turns out to be about a 0.05% in global cloud condensating nuclei (the seeds that form clouds).