In the Knoxville and surrounding areas, we rarely must deal with snow or ice and certainly not large amounts. That's great for protecting tree stems and branches. It can be a challenge for below ground issues as well as leading to a different kind of stress on trees that have evolved to 'shut-down' for a few months. We have rapid temperature fluctuations in temperature leading into the fall. This can lead to increased opportunities for pathogens infecting trees especially if those trees are cut/pruned too early. For most trees, you'll do best to wait until all the leaves have fallen before you have the canopy thinned and shaped. This will decrease the amount of above ground vascular (sap) flow which will reduce the probability of pathogen infection of critically important vascular tissues. This year, for example, oaks should have been pruned only during the winter because of the presence of a bacteria that clogs the piping (vascular) tissue of trees. No one could have known this until after the fact, but now, I recommend having your oak trees pruned (for the next several years) only during the dead-of-winter.
This is a terrible time to fertilizer your trees UNLESS you are using slow release fertilizers. This is the PERFECT TIME TO FERTILIZE deep in the soil with slow-release and/or biological fertilizers. Most of the resources are going being used for root growth so stimulate that process.
Keep your leaves and use them as a mulch around the base of your trees (keeping space around the base of the trunk). You can them work them into the soil in the early spring (or have someone do so) or remove them when you start our spring gardening. The leaves can protect your soils and roots near the soils' surface as well as provide a slow-nutrient release as they breakdown over the winter. If those leaves have fungal spores or bacteria that could cause problems during the growing season, then definitely have them removed. If, however, your plants have been healthy the previous year, using them is a free opportunity.
Needle cast and blight has been very bad this year on conifers (cypress, juniper, pi; have your conifers treated by a certified professional arborist throughout the year. A few years of treatment will allow your plants to regain their vigor and with proper soil/root care your trees' immune systems can be strengthened to improve their ability to fight these pests. Note, it is not uncommon for trees to be infected by multiple types of fungi and bacteria simultaneously, this is the norm.
Japanese beetles are best treated when they are under ground, as grubs. It's almost impossible to treat them during the spring and summer. They are capable of relatively long-flight. Killing the grubs during the winter is a far better strategy.
Winter is an excellent time (since our soils do not freeze or rarely so) to remediate high clay content and high soil pH (alkalinity). These treatments will last year’s benefiting every plant in your yard! Benefits that accrue to your pocket book;)