Styling an icon defined with prepend-icon in Vuetify

Target it properly and apply style.
For example in v-list-group:

.v-list__group__header__prepend-icon .v-icon {
    color: red;
}  

But note for example v-text-field append icon

.v-input__icon--append .v-icon { 
    color: purple;
}

NOTE: If it's not working, and you are using scoped styles, see how to resolve it.

Care not to use only .v-icon because for example you might override append icon as well, which might not be what you want.
Also, !important is not a good practice and we don't need to use it here.
So just rotate .v-list__group__header__prepend-icon class depending on component or even add your own class. Inspect element and see what the class is for prepend/append icon because it's not always same.
(if you are using scoped styles then perhaps there is no need for adding your own additional selectors for targeting the specific icons).

Example codepen

Note: I'm not aware of any vuetify's own classes or props for styling prepend/append icons. So if these exist or get implemented in the future, use them.

Using a v-icon inside the prependIcon slot of the v-list-group template (instead of the prepend-icon prop) will give you all the flexibility you need:

<v-list-group>
  <v-icon slot="prependIcon" large color="primary">comment</v-icon>
</v-list-group>

There's also an appendIcon slot available, btw. The official Vuetify documentation mentions the available slots, but is rather silent about any details.