I'm not sure what you read but I don't see anywhere that vampires aren't allowed to use fire magic. Fire spells do the most damage and are the most efficient, both things that are useful in close combat when you want to kill enemies quickly and aren't worried about hitting fast moving targets and slowing people down.
I went to Solstheim first to get Bound Dagger (killing the Ash Guardian is a real pain, bring follower(s)), and then traveled for a bit while progressing through the DB and College questlines.
I'm not sure what you read but I don't see anywhere that vampires aren't allowed to use fire magic. Fire spells do the most damage and are the most efficient, both things that are useful in close combat when you want to kill enemies quickly and aren't worried about hitting fast moving targets and slowing people down.
I went to Solstheim first to get Bound Dagger (killing the Ash Guardian is a real pain, bring follower(s)), and then traveled for a bit while progressing through the DB and College questlines.