From my experience you need to look at the winter buds which is great timing.
The buds of Ostrya are "usually" more divergent from the stem while the Carpinus the buds are "usually" tightly appressed to the stem. Juvenile morphology may be different however.
I guess the other factor is the Korean hornbeam is not native to your area, though I guess it could be naturalized, while the hop hornbeam is.