The Circle of Wildfire druid's Enhanced Bond feature states (UA: Cleric, Druid and Wizard, p. 3):
…In addition, when you cast a spell with a range other than self, the spell can originate from you or your wildfire spirit.
The rules on spell targeting state (PHB, p. 204):
To target something, you must have a clear path to it, so it can’t be behind total cover. If you place an area of effect at a point that you can’t see and an obstruction, such as a wall, is between you and that point, the point of origin comes into being on the near side of that obstruction.
Since the spell can originate from your Wildfire Spirit, whose senses would you use when casting a spell and having it originate from your Wildfire Spirit?
Would you require a clear path to the target from yourself or from the Wildfire Spirit?
Best Answer
RAW, only the caster needs a clear path to the target
Based on your quote on spell targeting, RAW, it would appear that you must be the one to have the clear path to the target, since you're the one doing the targeting; the Wildfire Spirit is just where the spell originates from once cast, and apparently does not require a clear path.
This is probably because, when such rules were written, there was no way to cast a spell from somewhere else (except via a familiar, but only with Touch spells, so that already took care of itself), since to have a clear path to target the target would also result in a clear path for the spell you just cast to reach the target.
Odd scenarios arising from this RAW reading
However, this leads to odd scenarios whereby your Wildfire Spirit could be blocked from your target (say, it's in a room, whilst you and your target are in a corridor just outside the room), and yet, you could cast something such that the spell originates from the Wildfire Spirit going through the obstruction at the target that you have a clear path to but your Wildfire Spirit does not (i.e. the target has total cover from the Wildfire Spirit).
For example, say you cast thorn whip at the target in the corridor whilst your Wildfire Spirit was still in this other room, which would then appear to leap out of the wall from the target's perspective, presumably then pulling the target into the wall.
The rules on cover (PHB, p. 196) says (bold italics emphasis mine):
So that first part of the quote implies that the "thorn whip through a wall" thing wouldn't happen, since the effect of thorn whip originates from the other side of the wall, but rather the thorn whip would just slam into the wall inside the room where the Wildfire Spirit is instead.
However, the second part of the quote that describes what total cover actually means talks about "targeting" again, simply stating that you can't be "targeted" by a spell, but if the druid and the target in the corridor have a clear path, then it can be targeted. That implies that, RAW, the odd thorn whip thing can happen after all, even though this certainly isn't RAI (Rules As Intended) or RAS (Rules As Sensible).
How to rule this sensibly as DM
It seems as though a DM would need to adjudicate this based on common sense. In other words, it's likely that for this to work, a DM could require both you and the Wildfire Spirit to have a clear path to the target; you to target it, and the Wildfire Spirit so that the spell's effect could plausibly reach the target.
However, this wouldn't matter as much if the spell itself didn't require a direct path (at least from a narrative perspective), such as frostbite, since I, at least, don't imagine that spell as having particle effects flying out of your hand and onto the target in the same way that I imagine ray of frost would look (although in that case, why bother making the spell originate from your Wildfire Spirit in the first place?).
Ultimately, it's up to the DM to make sense of this on a case-by-case basis.