Dragonborn is an LA +0 template from Races of the Dragon (an official book) with a bit of backstory and gp requirements, but it's fairly practical for a suitably rich level 1 character (100 gp, if memory serves).
Arctic, from Dragon Magazine (aka DrMag; semi-official) #306, is also an LA +0 template. Little bit more backstory. (Nothing to do with arctic orcs, the UA variant base race.)
Half-Minotaur is an LA +1 template from DrMag 313. Implies things about your fairly recent ancestry — you don't exactly have to have a parent that was a minotaur, but stretching it to a grandparent (and saying that your heritage was unusually strong for some reason) is about as far as you can usually go. Unfortunately, LA +1 means you can't have this at level 1, since you have to have at least one actual hit die/class level to be a character. Level 2 is fine though: you'd have one level adjustment and one "real" level to give you the necessary hit die to have any hit points, skill points, feats, and so forth. (The "real" level would be either a class level or a racial hit die. Usually a class level.)
Half-Ogre (also from DrMag 313; the Savage Species and Races of Destiny versions aren't any good for you, since they don't apply properly or have worse LA) would normally also be LA +1, ending up at +2 (and therefore a third-level character at minimum), but it has a somewhat odd LA entry that leaves it at +0 if you're already Large… which Half-Minotaur does for you anyway. More recent-ancestry implications.
Water orc is an Unearthed Arcana variant. LA +0. UA is official, but its variants are not in the base game by default; rather, the DM is supposed to pick and choose which variants they want to bring in. Variant races are generally fairly straightforward to allow in without changing anything else, although the elemental and environmental race variants are arguably a little tidier if they replace regular races/monsters rather than augmenting them; both choices are suggested in the book.
Upshot is that yes, it's legal (though rather dubious to many or most DMs), but only at level 2 or higher. At level 6, your group's starting level, you could very easily have all of these, assuming the DM was fine with that. In fact, using the variant LA buyoff rules from Unearthed Arcana, you could have bought off your LA and be a bit shy of level 6, but with almost enough XP to level again. Either way, you'd generally have 5 class levels and slightly less cash. A particularly generous DM might allow the backstory LA buyoff to have already paid for itself by larger XP awards from backstory adventuring, leaving you (compared to a normal ECL 6 character) 100 gp down, the product of some very unusual parents or perhaps a breeding program of some sort, and with a fat stack of stat bonuses and miscellaneous abilities.