In this context, "crabbed" means bitter, ill-tempered, or grouchy. "Age" refers to old age, and "youth" refers to young people.
The overall meaning of the line is that old people often are grumpy and critical with the activities or characteristics of young people (youth), due to old age or care, while the youths find old age annoying as it restricts, prevents and criticizes the things youths find joyful about life - "Youth is full of pleasance [pleasure], age is full of care". Shakespeare also contrasts youth with summer mornings with their warm air and freshness while comparing old age to cold and gloomy winter weather.