It's something to consider, people would expect Snow being there as a political statement and expect her to plot to further her agenda rather than thinking Homura as an independent.
Yeah, that's not something I had considered but is right up there with concerns. We would get similar problems with Mami, as she's considered to be Mitakihara's Ruler. So if we stick to girls that wouldn't give ideas of Homura as someone's political tool, we are limited to Oriko, Kirika, Ruki, Yuuma, Kyouko and if she's contracted by now Nagisa.
On that list, Nagisa is unknown where to find her so she's out or at least way way down my list of preferences.
Kyouko I hesitate to vote for simply because we have Arcana Kyouko to get her insights, and we will have to never use Arcana Kyouko during this trip if we bring present Kyouko. If we do not bring current timeline Kyouko, then we can get some minor element of surprise with having a "third" Puella Magi in play the court will not have had too much prior knowledge of. Doubly so if we bring Oriko and she's able to muddy the foresight ability of a hypothetical precog in Artoria's court. Though if we do use Arcana Kyouko in such a situation we do run some risk of offending the King by going around her "one contract escort" invitation, which brings Kyouko back up higher in the listing.
Macros thinks Oriko would send a similar message to using Snow (or Mami based on my earlier comment in this post), but I'm not really seeing how. Yes she's independent of Homura technically, but her actions are in support of Homura's goals, so unless you know Oriko well enough to get that information from her and know she's not playing you she should appear to be either a friend of Homura's or one of the Homu's subordinates. Especially if Oriko can and is willing to give some indication to Homura that any sudden actions she takes are part of her precog abilities so it looks like Homura is in charge. Really, Oriko's availability is the big question I see here on this one. Last we saw her she was helping Yuuma recover from being abused, contracting and apparent sudden memories of previous loops. But it has been a couple days so the healer may be up and ready now.
Yuuma's limitations are the same as mentioned with Oriko, plus Homura is unsure of her own relation with the greenette. For this I would put her very far down the list of candidates.
That leaves us with Ruki and Kirika to consider and think of where we prefer them. Ruki is a healer and has Homura flexing "Senpai muscles." But Ruki is inexperienced at Magical Girling in general and I would presume even less so at politicalling.
Kirika would likely be openly defiant whenever Homura isn't asking for something in-line with the girl's own desires and thoughts, unless given specific instructions by Oriko ahead of time.
So, for me, I think the list of preferences is something like this:
Oriko > Ruki > Kyouko/Kirika > Mami/Snow > Yuuma