CHICAGO—Relaxed and loose, some of the Tampa Bay Rays wore ski caps and earflaps for a workout Saturday, only to find sunny skies and crisp temperatures not requiring extra protection.

The Rays were ready for the elements. Then again, they were prepared for everything the Chicago White Sox did in the opening two games of their AL playoff series.

“You see a group of kids there—I won’t say happy just to be there—just like enjoying the moment,” said White Sox manager Ozzie Guillen, contrasting the demeanor of his veteran team and the younger Rays. “We have a veteran clubho...

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