Position rack in center of oven and preheat oven to 400 degrees.
Grease a 12 cup, nonstick muffin tin with the butter.
In a 4 cup liquid measuring cup, thoroughly whisk the cream and eggs. Whisk in the horseradish, 1 teaspoons salt, and a few grinds of pepper and set aside.
Portion half the bread cubes evenly among the 12 muffin cups. Portion half of the cheese and half of the chives evenly among the cups. Repeat with the remaining bread, cheese, and chives.
Whisk the custard again and carefully pour it into the muffin cups, distributing it evenly. Refrigerate for at least 30 minutes.
Bake until the puddings are set and the tops are nicly browned and puffed, 18-22 minutes. Let cool in the pan for 20 minutes. Carefully remove the puddings from the pan, running a paring knife around the edge of the puddings if they stick.
Can assemble puddings and refrigerate up to 6 hours before baking. Can also bake a day ahead, refrigerate, and reheat wrapped in foil, in a low oven.