Warm weather during the winter can be harmful in a couple of different ways. Frozen trees can thaw in the sun, especially where they face south. A sudden drop in temperature that can even be caused by a cloud covering the sun on a cold day can cause the warm bark on the tree to quickly freeze. These sudden changes can make the bark split, injuring and weakening the tree.
Large fluctuations in temperature in the ground can also cause soil to quickly expand and contract, sometimes making plants heave up out of the ground. This is mostly a problem for herbaceous perennials, especially those that are somewhat tender in our climate. As their roots become exposed to the cold winter air, they quickly die. Heavy mulch can keep the soil cooler during warm weather to prevent these types of fluctuations.
Dr. Ieuan Evans' helpful article How Cold Kills on page 46 of the 2007 Prairie Garden journal describes how warm spring weather is, according to Dr. Evans, the largest reason for supposed winterkill of trees and shrubs. As the days get longer, these plants prepare to break their winter dormancy, and some warm weather will often fool them into thinking spring has arrived, especially if they are native to a climate with a longer growing season than ours. The next cold snap, however, can quickly kill any actively growing plant parts. Again, heavy mulch can keep the soil cooler and keep these plants dormant longer. Planting on the north side of a slope or building can also keep the spring sun from warming their roots too early in the season.
Heavy mulch is often touted as the best way to overwinter tender plants, but armed with this information, it becomes clear why many gardeners recommend putting the mulch down after the ground has frozen - it is there as much to protect the soil from warm temperatures as from cold ones.