The rogue fails a saving throw (unless sculpt spells is used)
You are right: being unconscious / 0 HP is an auto-fail on Dexterity saves, if a save needed.
Unconscious (relevant point)
You are correct on the failed death save. (If damage is done).
Damage at 0 Hit Points.
If you take any damage while you have 0 hit points, you suffer a death saving throw failure. If the damage is from a critical hit, you suffer two failures instead. If the damage equals or exceeds your hit point maximum, you suffer instant death (Basic Rules, p. 76, Death Saving Throws)
But would damage have been done? Probably not.
Your ruling fits the spell's shape.
I like your ruling1. This kind of judgment call is what can add a lot of fun to a gaming session. Given the spell description, I'd say you were well within the rules. (See below).
As you hold your hands with thumbs touching and fingers spread, a thin sheet of flames shoots forth from your outstretched fingertips.
Further that point, if the wizard is from the Evocation School, and 2d level or higher, the "sculpt spell" feature would have allowed zero damage to happen to her even if she was in the area of effect.
School of Evocation
Beginning at 2nd level, you can
create pockets of relative safety within the effects of your evocation
spells. When you cast an evocation spell that affects other creatures
that you can see, you can choose a number of them equal to 1 + the
spell’s level. The chosen creatures automatically succeed on their
saving throws against the spell, and they take no damage if they would
normally take half damage on a successful save. (Basic Rules, p. 32).
1Taking into account the shape of the spell: a cone.
If you look at the spell description, Burning Hands is a cone.
Burning Hands; 1st-level evocation; Casting Time: 1 action; Range:
Self (15-foot cone); Components: V, S; Duration: Instantaneous
It is easy to argue that it is aimable in the Z-axis as well as in the the X and Y axes. If you adjust it as a caster, the wizard could aim the cone in such a way as to miss the prone Rogue and still hit the wolves. Your judgment call accommodated that spell shape without getting too much into simulation. Depending on what you judge as the degree of difficulty in so aiming, you may or may not wish to grant advantage to the saving throw the wolves make. (Thanks to @SeraphsWrath for raising this point)
That said, the spell's description and area of effect is a little unclear.(Cone, Basic Rules, p. 80)
As you hold your hands with thumbs touching and fingers spread, a thin
sheet of flames shoots forth from your outstretched fingertips. Each
creature in a 15-foot cone must make a Dexterity saving throw
So what is it? A cone or a thin sheet of flames? Since "sheet and cone" are both used in the spell description, the text is unclear and so we addressed this in detail in a different question. @Yakk points out that "a cone whose surface is a thin sheet of flames, but whose interior is empty, matches both descriptions used in the spell."