It, of course, depends on the type of fungus, but typically most fungi require respiration, nutrients (nitrogen or other minerals), water, light (but, not in most cases), and specific temperatures.
When it comes to plant disease, we refer to the plant disease triangle (I had to post it!)
A certain environment is needed for a plant disease to occur. Most plant pathogens that cause plant disease require a particular temperature, before they will sporulate or initiate infection. But, the bad news is just because fungal pathogens are not able to produce spores or infect your plants, does not mean that cold temperatures will wipe them out. In general, fungi can tolerate the range of temperatures that typically occur in the place where they have taken up residency. So, fungal disease pathogens that have made a home in Illinois, generally can tolerate our cold, winter temperatures. Fungi have figured out ways to survive during cold temperatures and, depending on the particular fungal pathogen, wait until just the right temperature to become active. Many plant disease pathogens produce special survival structures that are thick walled, which can survive extended cold periods as well as extremely dry conditions.
Many of our plant pathogens are lurking on diseased plant material in a dormant state, just waiting to attack a plant near you! Spring will bring warmer temperatures for fungi to become active once again. But, a more narrow range of temperatures may be required for a fungus to sporulate (produce spores) and this is one of the main ways a fungal pathogen can spread.
Don't forget that not all fungal disease pathogens overwinter here in Illinois. Rust spores blow up from the South and under the right conditions, can infect plant hosts during our growing season. However, a severe winter in the South, where rusts overwinter, could decrease the amount of spores that are blown into "our neck of the woods".