Can visible light be affected by magnetism?
I think you have cosmic rays and electromagnetic radiation a little mixed-up.
We all know that without Earths magnetic field, electromagnetic radiation from the sun would cook us within minutes.
No - the Earth's magnetic field protects us from cosmic rays. High energy charged sub-atomic particles, mostly from the sun. The Earth's atmosphere does protect us from Ultra-Violet radiation (i.e. light) which would kill us.
Since visible light is the same thing as cosmic rays, except that its a different wavelength,
No, cosmic rays are charged sub-atomic particles (protons, electrons etc). Visible light, and UV, x-rays, gamma-rays, infrared, are all electromagnetic radiation of different wavelengths
I was wondering if it were possible to use magnetic fields (they would have to be pretty strong) to essentially "block" light the same way it blocks cosmic rays?
Not directly. But magnetic fields do affect how light passes through certain materials. You can use this effect to make very fast shutters by passing light through a crystal and changing the magnetic field.
Apart from the misconceptions rectified in the other answers, here is an answer to the title of your question:
Yes, visible light can be affected by magnetic fields. A magnetic field can shift the lag between the clockwise and counterclockwise polarization component of light passing through a medium. This effect is known as the Faraday effect.
However, this does not allow you to directly block light, it only allows you to rotate the linear polarization of a light wave.
The medium can be very thin, if the distance is large enough (the magnetic field needs to be present over that distance as well), but there has to be some medium. Apparently it even happens in the interstellar medium and is used by astronomers to measure magnetic fields.
In vacuum, the answer is “Yes, but only with an extremely strong magnetic field.”
Light is an electromagnetic wave. Maxwell’s equations for the electromagnetic field are linear in the field strengths, so classically two electromagnetic fields just add together. This means, for example, that two light beams go right through each other without interacting, or a light beam goes through a static electric or magnetic field without interacting with it.
This is no longer the case in quantum electrodynamics, where quantum effects such as virtual electron and positron pairs in the vacuum introduce nonlinearities. The electromagnetic field is no longer purely additive. You can theoretically get scattering of light by light, and scattering of light by static electric and magnetic fields.
I don’t believe we have been able to observe this yet. This is because these nonlinear effects become significant only at enormous field strengths. The critical magnetic field strength is $m_e^2/e\hbar$ in natural units, or 4.4 billion Tesla. Magnetars have fields this strong, so we may be able to observe such effects astronomically.