Lightly butter the sides of a heavy 2 to 3-quart saucepan. In it, combine, sugar, milk, corn syrup, pumpkin and salt. Cook over medium heat, stirring constantly until sugar dissolves and mixture comes to a boil. Then cover the saucepan for 2 or 3 minutes.
Uncover, clip on candy thermometer and continue to cook over medium heat, stir as little as possible – just enough to keep the pumpkin solids from settling to the bottom of the pan. When mixture registers 235°F on the candy thermometer (soft ball stage), remove from heat. Add spices and butter that has been cut into ½ inch cubes. Do not stir or jar the mixture as butter is added or as the mixture cools.
When the mixture has cooled to 110°F, beat the mixture until it is very thick and loses some of its gloss. Use an electric mixer on low speed for about 8 minutes or beat vigorously with wooden spoon. Stir in nuts. Pour immediately into buttered 9-inch square pan. Score fudge while warm then cut when firm into about 80 pieces.