I thought they played well on Weekend #1, too, despite that Hope wasn’t in top-shape (I’ll see what I can find on Weekend #2). I mean, personally, I could get past her moodiness. But I know there were people who had a bad taste in their mouth from it. The only reason the set was underwhelming for me was that it did not carry the torch so well after a string of very fantastic performances, but even at the time, I was in need of a break.

Her comment from the stage Apr. 13, “Where’s the bartender”, reminds me of a comment she made a few years back at a San Francisco Warm Inventions show after experiencing repeated sound problems: “I need a glass of wine!” Sound problems are one of the things that get her stressed, & she’s been known to quit the stage over them.

So, “where’s the bartender” was perhaps her indirect way of saying she felt stressed &/or uncomfortable onstage at that moment about something(s), perhaps the cold, as you suggest. Also, she gets stage fright, & the massive sized audience may have felt intimidating.
She also gets stressed by bright stage lights, preferring near darkness. I think the stage lights were likely too bright for her Apr. 13.
On April 20, she reportedly made a point of requesting stage hands
turn down the lights, & you can see from YT clips of Apr. 20 that the stage is darker, likely making her feel less stressed. And it was much warmer Apr. 20.

Plus, on April 13 her voice was possibly stressed from her having sung in so many other shows just in the week leading up to Coachella weekend 1, & her voice may have needed a rest, which it received before weekend two, where she sounds better.

To my ears, the band played very well in both sets. The one difference
was Hope’s singing wasn’t quite up to par on weekend 1.
I’d like to find an audio &/or video recording of the full Mazzy weekend 2 set, as that was best of the two, apparently.