Can I add some softened gelatin to firm up mousse made with whipped cream?

I remember a tip in a baking cookbook, to add some butter to whipping cream to make it stiffer. Maybe was Rose Levy Beranbaum in her Baking Bible.
Another idea - don't use American pasteurized heavy cream, but either a British or French higher-than-35%-fat cream, lightly folded/mixed with the Nutella and chilled.

You can definitely add some gelatin. Mousse based cakes are often set this way so they remain light but hold in between the layers. I recommend using gelatin leaf in the same process boulangre suggested, it's gives a better texture than powdered I find.

I agree with adding the gelatin to the Nutella before folding in the whipped cream, as that is where the laxness of your set is lurking. Bloom a teaspoon of gelatin in 4 ounces of cream, then heat it over a low heat to dissolve the gelatin. If you don't melt it, it will be grainy in the end, and wll not give you the gentle set you seem to be wanting. You can tell that it is completely melted by pinching up a bit of the solution and rubbing it beteen your thumb and forefinger. If it feels sandy, the gelatin has not melted. Please let us know how this works for you. It sounds delicious.

The concept of adding gelatin to a mousse or custard is what makes a bavarian cream! If you're not looking for quite as set of a dessert, I would just add a tiny bit. I would also bloom the gelatin in a bit of the cream and whisk it into the nutella before adding the cream, then let it set in serving dishes.

I have often used gelatin to strengthen whipped cream, no reason why it shouldn't work here, but I've always added it to the partially whipped cream. There was an article on this site recently suggesting something else- cream cheese, I think- to make cream hold better. That might be relevant here, but I don't remember any details.