Years ago, we had several days of constant and cold rain in Utah. For the first day, we went "underground" and visited Timpanogos Caves National Monument, the second day we went to SLC and did the "mormon tour" including some time in the genealogical records archive and we had the good luck to hear the Tabernacle Choir at a rehearsal. But when the rain did not stop after that, we went south into the desert.
On a different trip, Glacier NP was deep in clouds and quite a lot of rain. There was not much to avoid it, so we put on our rain gear and did a short hike none the less.
Oh and the second coldest night I ever spend in a tent, was in Yellowstone in early June. We had about one inch of snow despite a decent weather forecast. We didn't get much sleep that night and went up pretty early. In the morning, the little bit of snow thawed very fast and we had an early start on a beautiful day.

I pout and throw tantrums.

We are avid day hikers but not campers, which shapes our Park visits. We both enjoy reading, like museums, and happily chat with strangers. We also tend to plan each trip with an extra day in case we want to just hang out or do something new we came across unexpectedly. We're also willing to hike in the rain and wander about with cameras in the snow. So a bad weather day is just another kind of day.
However, several times we've made reservations to stay over at Phantom Ranch in Grand Canyon, and the days we hike in and out are immovable. The last time we did this, there were high winds that made the hike down extremely unpleasant. It was like walking into a hair dryer. But we just sucked it up and hiked. We had the wonderful Phantom Ranch beef stew dinners reserved and waiting for us, plus dorm space and hot showers, and that was that. Flash floods or very heavy snows would have stopped us, but both were unlikely in late spring.

We find muddy river banks and pretend we're otters.  :)

Make "Lemonade" :).  Many times the challenges actually make the trip, if you are game.  A test (I like breakthroughs:).

Heck, I go out in it!!
Of course, sometimes with dubious results.
I hiked Shenandoah trails during on-and-off driving rain. Had all my raingear, was well protected, and had a ball. That is until I needed to go back up to the road. Had a wee bit o'trouble getting up the muddy trail. I was a filthy mess when I got back.
My trip to Denali, at the end of the season, ended at the same time the snow was beginning. You could see the snow on tops of the mountains when I got there, on day 2 it was a little further down, then a little further down, you could see winter approacing from the top! Capper was some good, old-fashioned snow squalls on the last day. In between, I saw Alaska in the fall, which IMO is the best time to visit.
Although I was intensely stupid when I went to the Painted Desert. Really enjoyed hiking through the geographically-amazing terrain, and when I got to the top, there was a thunderstorm off in the distance. The scene was straight out of a National Geographic magazine! Big, swooping thunderhead, lightning dancing side-to-side and up-and down, surrounding sky various shades of orange, red, and deep purple, all set against the harsh terrain of the Painted Desert!
Wonderful, until I realized that I was the highest point in the land!! High-tailed it to the car at that point ...

There's no such thing as uncooperative weather, merely uncooperative clothing!