Learn Polish: W przeciwieństwie do zeszłego roku lato jest zimne. - In contrast to last year, the summer is cold.

The phrase w przeciwieństwie do means "in contrast to" or "unlike". The preposition do always forces the following words into the genitive case. So, instead of the locative w zeszłym roku that you use to say "in last year", you must use the genitive zeszłego roku to match the preposition.

I learned that "it is cold" is jest zimno. Why does this sentence use zimne instead?

You use the adverb zimno for general environmental states, like dzisiaj jest zimno (it is cold today). However, here you are directly describing a specific noun (lato). Because lato is a neuter noun in the nominative case, you must use the matching neuter adjective zimne.

What is the base form of przeciwieństwie?

The base dictionary form is przeciwieństwo (opposite or contrast), which is a neuter noun. In this sentence, it takes the locative case because it follows the preposition w. The entire phrase w przeciwieństwie do is a very common fixed expression that is great to memorize as a single chunk.

Shouldn't there be a comma after roku to separate the introductory phrase, just like in English?

No, Polish punctuation rules differ from English here. In Polish, you generally do not use a comma to separate a prepositional phrase at the beginning of a sentence from the main clause, even if you naturally pause there when speaking.