You might want to consider burning them, too (fire I spell). When the fire runs out on its own, a burnt forest appears -> new forest -> forest -> (with FoL) ancient forest. Buiding improvements into burnt & new forests is quicker than on forests, and can be done by all civs (bug). Note: putting out fires with the spring spell inhibits the forresting process (bug, also reported in the bug thread a while ago but no changes made AFAIK)