It rather depends upon the frosting. Buttercream and cream cheese frostings will do okay when frozen; whipped cream frosting will not. It will melt and make a mess when thawed.
If you want to freeze the cake to save it for later, freeze it unwrapped on a tray, and wrap after it's frozen. That way, the frosting won't get glued to the foil or wrapping paper. You do want to wrap it, so it doesn't get all dried out.
Then, when you want to eat it, take it from the freezer, and remove the wrapping before allowing it to thaw, again, so the frosting stays on the cake instead of the wrapping.
However, freezing "naked" cakes is easily and often done--even by professional cake decorators, who will often freeze a cake prior to frosting it, as a way to prevent too many crumbs from getting into the icing. The surface crumbs are then easily brushed away, without causing more of the cake to turn into crumbs. (Because, think about it: trying to remove ALL the crumbs from a cake would be about as easy as trying to remove ALL the strings from celery!)