Learn Russian: Зимний день короткий.

In Russian, the present tense of the verb 'to be' (am, is, are) is usually left out. So, Зимний день короткий literally translates to 'Winter day short'.

How do we know to use the masculine adjectives зимний and короткий here?

Adjectives must match the gender of the noun they describe. The noun день (day) is masculine, even though it ends in a soft sign (ь). Because of this, both adjectives describing it take their masculine forms.

Why do both зимний and короткий end in -ий instead of the standard masculine ending -ый?

They both end in -ий, but for different reasons! Зимний is a 'soft' adjective, meaning its base naturally takes soft endings like -ий. Короткий ends in -к, which triggers a strict Russian spelling rule: after the letters к, г, х, ж, ч, ш, and щ, you must always write и instead of ы.