Gee, why not?
...but I guess electric fields don't affect light either.
hmm, seems that 'why' is a bit of a tricky question so instead i will try to focus on 'what';
particles affect other particles via fields and waves.
light waves are not affected by fields.
(waves which are cosidered particles in quantum mechanics, but are fundamentally different from 'normal' particles as they have zero rest mass)
(waves are cuved by gravity according to general relativity, but that is a result of the curvature of space-time, rather then a force acting on a particle)
Light propagation is characterized by alternating electric and magnetic fields ...or something like that, right?
yes that is persisely right.
Electric and magnetic components are perpendicular to each other, with sine wave ...nature.
once again percicely right 
Are the electric and magnetic peaks in phase with each other?
yes
Yes, of course they are (well I'll assume....)
So my problem is that I picture a field as 3 dimensional, say like a doughnut or....
an electric field is 3-D and a simple representation such a field that is generated by a positive point charge can be found here http://www.geocities.com/rmazzio/U6ExamImage1.gif
a magnetic fiels is also 3-D but is a bit more tricky since it has a south and north pole it looks like this:
http://www.magnetic-shield.com/image...lux-images.jpg
...but then why doesn't it overlap with the magnetic 3-D field...?
it does overlap, and as a result the changing magnetic field generates the electric field and visa versa
I guess I need to learn more about what polarization detects....
...the orientation of the fields, not the fields themselves....
polarization is interesting, but not nessesary in order to understand light. a good 3-D representation of light's elecrtic and magnetic fields can be found here.
File:Onde electromagnetique.svg - Wikipedia, the free encyclopedia
hmmmm. Any comments, thoughts, guidance, suggestions, opinions, etc.?
...but then why don't other magnetic fields affect light? Is is just one dimension of a magnetic field that is being propagated, or a whole 3-D field?
umm this is a bit of a tricky one. perhaps you can try to work out *how* electric and magnetic fields affect charged particles, then you will see that the rules cannot be applied to light 
i hope this will make thigs a bit less confusing
