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Since you are in zone 4, you can either wait till spring to cut the branch off the main plant or you can cut it from the mother plant now and overwinter it indoors. Cut it but don't dig it up for a couple of weeks. Let it continue to grow roots on its own before it is uprooted. Then place it in a container with potting soil. Overwinter the container in the garage or somewhere that stays above freezing till spring. It will only need water about once or twice a month indoors. Too much water will cause it to rot. In spring, after the danger of frost is past, you can plant it outside.

Fort Mill, SC, recently experienced its first frost on October 31, 2024, with temperatures dipping to 31°F, which is just below freezing. Prior to a frost, you can water deeply the night before and also ensure you have 3 to 4 inches of organic mulch past the drip line. You can let the leaves fall on their own. For varieties that bloom on old wood and thus now have flower buds at the stem endings, this may be enough in mild winters. If your variety is not bloom reliable or if temperatures wildly fluctuate and crash well below freezing, consider winter protection. You can search YouTube for “hydrangea winter protection” to see videos of various methods.

Big Leaf Hydrangeas will break dormancy in two separate stages. Brand new spring 2025 stems will first break dormancy and grow from the base/crown of stems. Leafless stems will then break dormancy about 1-2 months later, leaf out and bloom. Thus, aim not to prune all the way down any 2024 leafless stems that remain leafless until the end of May or later.

For a La Niña Winter, expect drier and warmer conditions. If the soil is dry at a depth of 4”, water deeply. Maintain 3-5” of organic mulch at all times of the year.

I'd leave all pruning for spring. Otherwise, it'll be the next year before it flowers properly. This collection of articles will help with the care of your Hydrangea:

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea

Please do not put your personal information out to the public. I have removed it for you. For hydrangeas in your area, I would look at individual cultivars. Usually, if you find them in your area, they will grow. I'd start with searching cultivars that appeal to you first. If they happen to be in your zone, then you are in luck. If not, you will need to keep on the search!

For now, this will help you find one that is suitable for your area: https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-9-10-11/zone-9-hydrangeas.htm

Since it gets so cold there, and hot in summer, mulching under the shrub would help it thrive.

Panicle hydrangeas and smooth hydrangeas can survive in zones 3 and 4. Eight hours of direct sun hopefully won't be too much. If so, you may need to water more often. (mulch would help here, too) Look for hydrangeas with the second part of the name as "paniculata" or "arborescens."

For example Hydrangea arborescens 'Hills of Snow' or Hydrangea paniculata 'Bobo.'

I've included an article that shows several photos. I think you would like the Annabelle hydrangeas.

https://plants.ces.ncsu.edu/garden_detail/hydrangeas-in-the-garden/

https://plants.ces.ncsu.edu/plants/hydrangea-arborescens/

https://extension.umn.edu/planting-and-growing-guides/pruning-hydrangeas-best-bloom

It could be that you have the macrophylla type that blooms on old wood like you say. Trimming it in fall would indeed cut off the blooms. Do not prune again till it blooms. Then if needed you can prune soon afterwards.

Lack of light can be a problem, too. Most hydrangeas need at least partial sun. Here is more about why a hydrangea may not bloom:

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-not-blooming.htm