Well blight is a fungus, so I suppose it possible spores could remain on the cage. Both options could damage metal, but not that much. Use mulch next year to keep soil spashes down. I use pine hay, as I have an unlimited supply. Works well for gardens and pots.

I don't know what you mean by blight. People use that word to describe all sorts of fungal and bacterial diseases that effect tomatoes. It looks like you're in Illinois, and according to USAblight.org, there were no reports of late blight in your area, so it's unlikely to be that. It's more likely alternaria, sometimes called Early Blight. You might want to read the other thread on this forum called Spray regime for tomatoes. There's a long passage copied from Dr. Carolyn Male that describes the different tomato diseases.

On your specific question, most tomato diseases cannot survive winter on a tomato cage. To be safe, you could wipe down your cages with soapy water or diluted (10-1) bleach or vinegar. But don't risk hurting yourself with straight bleach or fire.