It's not going to hurt the trees if it gets frost again. The buds will die and new ones appear when the proper time comes. Seen that many times before.
Well, I not gonna’ claim to be an expert, but I’m not so sure about that. At the same time, I’m not gonna’ say you’re wrong either because I can’t seem to find a definitive answer. The thing is, those trees are likely to see an extended deep-freeze, not just a period of frost.
Back a few years ago we had an unusually warm period in March/April which resulted in early bud break of maples and oaks. Then a hard frost period in May caused considerable frost damage (deformed leaves, dead twigs, etc.). Some of those trees dropped the damage and produced new buds; some just lived with the damage for the season duration… overall, new growth that year was limited and not much for fruit/seed. But a bud break in January ain’t the same thing…
This far north, when trees begin the transformation into hibernation, an internal chemical change happens, engineered to protect the tree from extreme cold. Trees dump water from their cells and begin to produce “anti-freeze” enzymes and compounds that protect the cells from freezing and keep cell walls flexible during extended
sub-zero (not frost) conditions. This “change” happens slowly, beginning in August and lasting through November, or even into December. Before the buds can break this “change” must be reversed to some greater or lesser degree depending on species (i.e. the sap starts to run). Trees “breaking bud” in January have reversed their “anti-freeze” protection… If the weather pattern now suddenly switches to normal January/February/March temperatures those trees will be un-protected from extended sub-zero periods. What I can’t seem to find is what the effects of that sort of damage will be… it seems we’ve never had a (recorded) early January “bud break” before.
Strange… very strange…
