hard time vs rough sledding

hard time and rough sledding both are nouns.

Word	Noun	Adjective	Verb	Adverb
hard time	Yes	No	No	No
rough sledding	Yes	No	No	No

As nouns, hard time and rough sledding are synonyms defined as:

hard time and rough sledding: a difficulty that can be overcome with effort

hard time (noun)	rough sledding (noun)
a difficulty that can be overcome with effort	a difficulty that can be overcome with effort
a term served in a maximum security prison