In a 3- to 4-quart pan over medium heat, stir marshmallows with half-and-half until melted, about 5 minutes.
Nest pan in ice water; stir often until cool, about 3 minutes. Add lime peel, lime juice, and tequila; stir occasionally until cold, 8 to 10 minutes.
In a food processor, whirl cookies until finely ground. Add butter and whirl until mixed. Press cookie mixture evenly over bottom and halfway up sides of a 9-inch cake pan with removable rim.
In a bowl with a mixer on high speed, whip cream with sugar until it holds soft peaks. Fold in marshmallow mixture, blending well.
Pour filling into crust and spread level. Freeze until firm to touch in the center, about 1 hour, then wrap airtight and freeze until solid, at least 2 hours longer or up to 2 weeks.
Unwrap pie, run a thin knife between crust and pan rim, and remove rim. Set dessert on a flat plate. Let stand at room temperature about 10 minutes to soften slightly, then cut into wedges.