Daikan (Greater Cold): it's the day of the year when the cold is most severe — and yet you could also say that spring is fast approaching.

Literal

Greater-Cold: 1-year [in-で] most coldness [subject-が] becomes-severe day [copula-です]-but-が, spring [subject-が] soon immediately approaching [quotative-と] also can-say.

Gloss-definition format (term + colon + description) common in dictionary and calendar entries. 大寒 is one of the 二十四節気 (24 solar terms) of the traditional East Asian calendar — the period around January 20 when the cold is said to peak. ~とも言える ('it can also be said that') is a characteristic written-language hedging construction. 間近に迫る is a set phrase 'to be fast approaching, right around the corner.' The mid-sentence が is the soft contrastive 'but/and,' not the subject marker.