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Absolutely! You can take hardwood cuttings or softwood cuttings. Here is an article that will explain these processes:

https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

Some browning is normal in hinoki cypress during the winter and it is hardy to zone 5, so I think it will be OK. The leaves will shed and should regrow. If nothing changes by about June or July, it likely did not make it.

Even 8 degrees F is included in your zone 7b, so your plants should recover. Wait till after all threats of frost have passed in spring before doing any pruning. Here is more:

https://www.gardeningknowhow.com/ornamental/trees/tgen/winter-damaged-trees-shrubs.htm

https://www.gardeningknowhow.com/ornamental/trees/false-cypress/growing-hinoki-cypress.htm

You are on the edge of its hardiness zone so there may be some issues with cold tolerance. Here are some other trees for privacy in your zone 5 that tolerate more cold.

https://www.gardeningknowhow.com/garden-how-to/garden-by-region/east-north-central/growing-north-central-coniferous-plants.htm

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-5/zone-5-evergreen-trees.htm

It could be cypress tip moth damage. You can prune off the dead foliage. Here is more:

https://www.gardeningknowhow.com/plant-problems/pests/insects/cypress-tip-moth-control.htm