Lloviznando is the conjugation of the lloviznar that stands for the present progressive. The present progressive is used when talking about something that is happening now. Verbs in the present progressive often comes after conjugations of the verb estar. In this sentence, está is the conjugation of this verb that matches the third person singular. Finally:
<em><u>Valeria:</u></em><em> ¿Cómo está el clima hoy? </em>
<em><u>Carmen:</u></em><em> Está templado pero está </em><em>lloviznando.</em><em> </em>