I have noticed damaged leaves on many trees after recent frost and cold temperatures, are the trees OK?

The answer could be yes, or no. Older established trees will often recover just fine. Newly planted trees could have problems. These trees are already stressed from transplanting, which results in a loss of roots. It takes a few years for these trees to re-grow roots to the same density as before digging. These plants are definitely going to need more care to recover. Watering these trees more often when dry will help new leaves to develop. Keeping these plants insect and disease free will also add to the effort. There is also a chance very old and stressed or diseased trees will not recover. The defoliation caused by frost will further the state of decline in these trees. Since trees are too big to cover during frost periods, there is hardly any prevention other than proper watering before and after frosts. Most of the damage recovery is a wait and see for a few months after.