I've only seen a few high-quality research studies on the anti-fungal properties of honey, but they suggest that many different types of molecules in honey may be involved with this anti-fungal effect. For example, some honey (particularly honey from darker honeycombs) contains propolis, a complicated resin-like substance that is sometimes called "bee glue." Many aromatic acids, as well as benzyl cinnamate, methyl cinnamate, caffeic acid, cinnamyl cinnamate, cinnamoylglcine, terpenoids, and other molecules are contained in propolis, and all of these may be involved in its anti-fungal activity. In addition, there may be special proteins in honey that have this kind of property.
I haven't seen studies that report nutrient changes following the cooking versus freezing of honey. In general, however, heat and cold have very different effects on the nutritional value of food. There is almost always more nutrient loss with heat than with cold. Heating would be likely to damage most, if not all, of the beneficial molecules found in honey. Freezing would damage some of these molecules but not others. If you were to compare freezing to cooking honey, freezing would definitely have the lesser impact of the two processes.
It is also important to remember that the overall quality of the honey is very important and organically produced honey is the best choice in this regard. In fact, I would feel better about the purchase of a high-quality, organically produced but pasteurized honey than I would about the purchase of a raw honey of unknown quality.