Wood frogs are highly philopatric to their breeding ponds. And the fact that they return to the same pond after multiple winters, would indicate that, at the very least, they must retain at least some spatial memory after freezing.
It is worth noting that a frozen wood frog is not nearly the same scenario as a butterfly metamorphing. Butterfly metamorphosis involves complex reintegration of all bodily systems, whereas frog brains do not reform during the winter--they just cease neurological activity. Even frog metamorphosis is less complex since much of the chondocranium and brain morphology is retained from tadpole to frog.
I know it wasn't the original question, but it is relevant to note that tadpoles seem to retain their personality through metamorphosis (see Wilson & Krause, 2012; Koenig & Ousterhout, 2018), which also seems to indicate that they have neurological stability.
Wilson, A. D. M., & Krause, J. (2012). Personality and metamorphosis: is behavioral variation consistent across ontogenetic niche shifts? Behavioral Ecology: Official Journal of the International Society for Behavioral Ecology, 23(6), 1316–1323.
Koenig, A. M., & Ousterhout, B. H. (2018). Behavioral syndrome persists over metamorphosis in a pond-breeding amphibian. Behavioral Ecology and Sociobiology, 72(12), 184.