「凛」 is another word for ‘cold’ in japanese.
「として」 being a way of binding sentences and compare: «X as Y»
時雨 is a combination of the kanji for time 「時」and rain 「雨」
I’m not sure what word these two kanji’s together make, but I’ve looked it up and it translates into drizzle or shower in late autumn/early winter.
Drizzle, being light rain in small drops - seems like it could make sense, but still, I’m not sure how the combination of time and rain can make drizzle.
In other words: shower (as in rain shower) in late autumn/early winter - sounds more accurate. We know it’s towards cold times and it makes sense that the word cold is used for comparison.
We know that many things in japanese, can’t be translated into an english word. Another example of this is 「口寂しい」(kuchisabishii) which directly translates into «mouth lonely» and it’s used as an expression for when you eat, because your mouth is lonely. In japanese it’s a word, but in english it turns into a sentence.
「時雨」is the same, and can’t be translated into a direct word in english, and therefore becomes a sentence. I guess the kanji combinations doesn’t always make sense for us who aren’t japanese, but still - time and rain can clearly give a hint that it’s about rain at a spesific time.
The translation of 「凛として時雨」might be «cold as the shower in late autumn». Or more gramatically correct; «cold as the late autumn rain».
Hope it helps!