"through" has the feeling of into something. For example, "The fog spread through the crowd" would create the image that the fog is in between the people in the crowd. "Over" has the feeling of being above or on top of. For example, "The fog spread over the crowd" would create the image that the fog is above the people (not in the crowd). I hope this helps!

Spread through means to spread or pervade throughout. Spread over means to spread something across and cover something.

I would use "spread through" in a sentence like "The aroma of the roasting meat spread through the house" and "spread over" in one like "Spread the butter over the bread." To use some cooking examples :).