DES MOINES, Iowa—A patch of muddy parkland was transformed Saturday into a test laboratory for how to win the first round of Democratic presidential-nomination balloting, while a new poll showed Sen. Elizabeth Warren ahead of former Vice President Joe Biden for the first time in this influential state.

An Iowa poll of likely Democratic caucus-goers sponsored by the Des Moines Register, CNN and Mediacom released Saturday evening showed Ms. Warren of Massachusetts leading Mr. Biden, 22% to 20%. They were followed by Sen. Bernie...