Learn German: Es war draußen eisig, umso schöner tanzten die Schneeflocken. - It was icy outside; the snowflakes danced all the more beautifully.

In this structure, the combination of umso and the comparative word (schöner) takes up the entire first position of the clause. Because this is an independent main clause, the verb (tanzten) must take the second position to satisfy the V2 rule, followed immediately by the subject (die Schneeflocken).

Is this the same grammar as the je ..., umso ... (the ..., the ...) structure?

It uses the same word, but the sentence structure is different. A je ..., umso ... sentence uses a dependent clause followed by a main clause. Here, both clauses are independent. The umso in this sentence translates to "all the more," showing that the fact established in the first clause (it was icy) makes the action in the second clause (the beautiful dancing) even more intense.

Why doesn't schöner have a declension ending here, like schönere?

Because it is acting as an adverb here, describing the verb tanzten (how the snowflakes danced), rather than modifying a noun directly. In German, comparative adverbs look exactly the same as the base comparative adjective, with no extra endings.

Could I use desto instead of umso in this sentence?