In a large pot, melt the butter over medium-low heat. Once the butter is almost completely melted, add the marshmallows.
Stir to coat the marshmallows fully in the butter. Cook for 5 to 8 minutes, stirring intermittently until the marshmallows melt completely. Don't overcook, as this will cause the mixture to burn and the marshmallows to harden.
Remove the pot from the heat. Stir in vanilla extract and salt.
Pour in the cereal. Stir to fully combine, making sure to scrape any additional marshmallows from the bottom of the pot.
Place a 4-inch round cookie cutter on a plate or parchment paper. Carefully scoop some of the marshmallow and cereal mixture into the cutter until it's full and the mixture takes the form of the circle.
Allow to cool for 5 minutes, then remove the treat and set it aside. Continue with the rest of the mixture until all of it is shaped into 12 equal-sized circles.
Add chocolate chips to a plastic zip-top bag. Melt in 30 second intervals in the microwave until smooth. Snip a small corner off the bag. Use the melted chocolate as the glue to hold on the other decorations.
Carefully cut the orange m&ms in half. Working with 1 treat at a time, add a dot of melted chocolate to the center of the rice krispie treat and gently press the halved m&m cut side down on the chocolate until it sticks.
Place 2 small dots of melted chocolate above the orange m&m and quickly press 2 brown m&ms into the chocolate until they stick to create the snowman's eyes. (Make sure to place the m&ms upside down so the logo "m" does not show.)
Place 5 small dots of melted chocolate below the orange m&m in the shape of a half circle for the snowman's smile. Press 5 brown m&ms into the chocolate until they stick.
Cut the candy strings into 4½-inch pieces. Flatten the ends of the string by pressing it between your fingers. Place a small dot of chocolate on each flattened end and then stick the string to the top of the snowman's head.
Using 2 of the same colored m&ms, place a chocolate dot on each before pressing one on both ends of the candy string to form earmuffs.
Repeat until you've finished decorating the rest of the snowmen. Allow all the chocolate to harden before moving, stacking, or serving.