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You can use Neem Oil to treat the plant and soil.

This will act as a insecticide and fungicide.

Here are a few links for you.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-winter-care-how-to-protect-hydrangeas-from-winter-cold-and-wind.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

I like to check the pots throughout the winter months.
You can add a bit of moisture each month to keep the soil from drying out completely.
Add a few inches of leaves or wood chips mulch to the top of the pot to help with moisture retention.
You want the pot to stay in a fairly constant temperature. Cold is good and below freezing is fine.
Thawing and then refreezing is harmful to the roots.

The brown leaf edges can be caused by watering issues. If they plant is let to dry out and then watered, it can cause the leaf edges to turn brown.

Keep the container Hydrangea consistently watered.

Excess fertilizer can also cause the edges of leaves to turn brown/black.

The white spots are most likely powdery mildew. For more information on powdery mildew and a course of treatment, please visit the following link:
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

Hydrangea need plenty of morning sunshine and then afternoon shade when in containers.
Check the soil daily. It should be moist but never soggy. Let the top inch of soil dry between waterings. In warm weather you may need to water twice a day. Make sure excess water can drain from the container.

Hydrangea can suffer from wilt if they are in the hot sunshine.
You an fertilize your potted Hydrangea with a water soluble fertilizer with a 20-20-20 formulation.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-container-care.htm

Recommendations for winter protection depend on the lowest temperature that your region typically experiences each winter. In Toronto, it looks like some species (Hydrangea aspera and microphylla) do need protection because some nights reach below 0 degrees F but not below -10 degrees F. Additionally, potted plants are more sensitive to cold.

Recommended protection methods involve surrounding the plant and pot with a frame or metal cage, filling the cage to surround the plant with leaves or straw, then placing a plastic bag or row cover over the whole thing. Or, for potted plants, you can simply bring them indoors. Here is more:

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-winter-care-how-to-protect-hydrangeas-from-winter-cold-and-wind.htm