If you are doing a Frozen theme, I assume you want a white, not chocolate frosting.
American buttercream is tooth-achingly sweet, but it holds color and decorations better than any of the others. It's basically just powdered sugar, butter & milk. It's the simplest to make.
French buttercream is over-the-top rich with butter and egg yolks, very soft, has a pale yellow color, and doesn't take either color or stiff decorating well. Because of the high butter content it does not hold up in the heat. It's also the most PITA to make of all the buttercreams.
Swiss meringue buttercream is soft, very white, light, and pretty sweet, though not as sweet as American. It is too soft for elaborate decorations. It's a meringue with butter beaten in.
Italian meringue buttercream is stiffer than Swiss, but similar in color. Also a meringue with butter added, but technique is different from Swiss. Still kind of soft for elaborate decorating.
German Buttercream is a combination of pastry cream or custard base and butter. It tastes similar to whipped cream, and less sweet than most buttercreams. It must be kept chilled, especially in the summer.
Ermine Frosting, also known as Flour Buttercream, is also less sweet. It's soft & fluffy, and spreads beautifully. Because of the flour base, it holds up better in warmer weather. Stella Parks on Serious Eats has a good recipe.
If I were doing Frozen themed cupcakes, I would probably frost them in a not-too-sweet Ermine Buttercream, and use American Buttercream for any fancy decorations. Most bakery/grocery store cakes use their better tasting icings for the cake, and a powdered sugar based frosting to color & decorate. It's a little more work to make 2, but the results are much better.