No it was fine. We actually went to the first party of 2023 so it was around May 22nd or so.
I'm super sensitive to the cold and it was probably a tad chilly for a minute when you get out of the lazy river but then you get used to it. I also wear sort of a skirted swim leggings & a swim shirt and they stay wet a bit longer than bare skin might...which doesn't make me warmer haha!
The weather for that trip was great - it was hot but not the summer heat.
Also to your other question - I think there's no refunds unless the party is cancelled due to weather. My guess it kind of works like the other Disney special event evening parties. Not sure what they'd do if a party started but big storms came and everything shut down for most of the evening - my guess is if you complained they might give you a credit for the ticket or something. It's a good question.
We went last year at 6pm and went straight in the water. We planned to get the free drinks and treats later in the evening. Big mistake.
At 8:30 pm a big storm blew up. Thunder, lightning, driving rain. We huddled under what cover we could find by the Typhoon Lagoon gift shop until after 9pm waiting for the rain to completely stop

. It never really did, so we gave up and left. Or tried to leave anyway
We then changed into street clothes to wait over an hour in the storm with a huge crowd at the Typhoon Lagoon bus stop for room on a space available bus.
That bus then dropped us off at Disney Springs, where we waited wet and shivering for another bus to get back to our resort. Got back to our room around midnight.
We should have called an Uber from Typhoon Lagoon, had we realized what a nightmare it would turn out to be to get back to our resort.
Various cast members along the way told us that once the storm began Disney sent out a bunch of buses to each park and bus demand just exceeded supply.
The funny thing is that there was no rain in the forecast and we had ponchos back at the resort! We can laugh now about our series of unfortunate events Typhoon Lagoon H2O party, way, way too much H2O!
No refunds were available.