Learn Polish: Zimą nocą mróz jest bardzo silny. - In the winter at night, the frost is very strong.

They are in the Instrumental case. Polish often uses the bare Instrumental case (without a preposition) to express when something happens during a specific season or time of day. This turns the noun zima (winter) into zimą (in the winter) and noc (night) into nocą (at night).

I learned earlier that at night is w nocy. Is nocą exactly the same thing?

They mean the same thing, but they have a slightly different feel. The phrase w nocy is the standard, everyday way to say at night. Using the bare Instrumental nocą sounds slightly more descriptive, general, or even poetic, much like saying by night in English.

Can I stack these time words in any order, like nocą zimą instead of Zimą nocą?

While people would understand you, it sounds much more natural in Polish to put the broader time frame first, followed by the more specific one. So it is best to start with the season (Zimą) and narrow it down to the time of day (nocą).

Why is the frost described as silny instead of ciężki (heavy) or twardy (hard) like it might be in English?