I think the best answer is sort of like will so-and-so mind if I try to reschedule our appointment to go to (fill-in-the-blank-here). Because there are hundreds of companies and even more schedulers, it depends.
Some shops like car washes and outdoor events are weather dependent. So rescheduling for these is expected at times. At the other end of the spectrum are companies and schedulers that are very rigid and want shoppers to hold to the promises they make without variation. They might hold it against someone who has a history of rescheduling. Thankfully, those types are not prevalent.
When you think of rescheduling or asking for an extension, keep in mind your relationship with that company.
Happily shopping Rhode Island and nearby Massachusetts and Connecticut
I did it a few times this year to dodge projected blizzards. I sent a message from the shop, said that I hoped it was OK, and went out and did the shop. Luckily the scheduler in question was in Boston. I think they got the record for this year, topping out at over 100 inches.
I am not going to fight with snow for this type of money. Another shop wound up being later than I had projected. Our road are torn up and completely pothole laden. It got dark, I couldn't see the potholes well enough to dodge them and was on a road with a fairly high speed limit. I was starting to get shaky as I drove. I came home, sent a message, called the next day and did the shop while it was daylight.
I like the shops that have date ranges of several days or shops that say anytime from now until the deadline. The prophet shop system is more likely to offer that.
If I want to reschedule to fit in a better job that is date locked on a smaller jobs date, I will offer to do the job sooner than the scheduled date. Unless the client has a guideline that it must be a Friday night or some other restriction, the scheduler usually loves the idea of an offer to push the shop date up. This way if you flake, they have more time to get it rescheduled before the true due date.