In a medium metal bowl sprinkle gelatin over cold water to soften 1 minute. Whisk in yolks and sugar and set bowl over a saucepan of simmering water. Cook egg mixture, whisking constantly, until an instant-read thermometer inserted 2 inches into mixture registers 160°F. (Tilt bowl to facilitate measuring temperature.) Remove bowl from pan and with an electric mixer beat egg mixture until cool and thickened, about 5 minutes (mixture will be very sticky). Beat in pumpkin and spices. Chill pumpkin mixture, covered, until thickened and cool but not set, about 1 hour.
In a bowl with cleaned beaters beat cream with vanilla until it just holds stiff peaks and fold into pumpkin mixture gently but thoroughly. Coarsely crumble 2 gingersnaps into each of 6 Martini glasses (or other 6- to 8-ounce stemmed glasses). Transfer mousse to a large pastry bag fitted with a large plain tip and pipe decoratively over cookies in glasses (or simply spoon mousse into glasses). Chill mousses, uncovered, until firm, about 3 hours, and up to 1 day (loosely cover after 3 hours).
Just before serving, garnish mousses with remaining 6 whole gingersnaps.