It's an old joke amongst homeschoolers: They never get a snow day. If the weather is bad, that's practically IDEAL homeschool weather. Look kids, you can't go outside, might as well get some work done.
What homeschoolers do get is sunny days! We are much more likely to take off when the weather is pretty and we can enjoy the great outdoors. But the weather does affect homeschool. Actually, it's something you need to learn to work around.
In our former life, our oldest daughter attended both public and private school. The school calendar ran our family's schedule. When they were open---there was school. And then they closed for bad weather---we had to adjust. But in the world of homeschooling, it's all up to me. I'm the one who has to be the adult and say "No, we are getting some school work done today even though it is pretty outside" or "Forget school, go out and play!" It's harder than you might think to make that call.
I have rarely regretted blowing school off for a special day. Then again, I'm pretty good at having school regularly, so those days are rare. While it is true that school can be done in the evenings, on the weekends, or whenever, my children hate that. They much prefer getting it knocked out early in the day and only Monday-Friday when Daddy is at work. So we are pretty good at getting school done most days, regardless of the weather.
Around here, we don't have snow days because we are just simply too far south. Hurricane days? Now those we have. (And yes, I've even made my children work during a hurricane and during a power outage. I'm tough.) The best plan of action I've found, to avoid making that call each time the weather changes, is to build some flex days into your school year schedule.
If you plan out your year so that you know you have a certain number of "extra" days, then you will be assured of that freedom to take off when the mood strikes. It's not necessary that the kids know you have those flex days. You can just go on letting them think that mom is the coolest for letting them off sometimes. But you will have the peace of mind to know that while you are enjoying a crowd-free beach day, you aren't getting hopelessly behind on lessons.
It's not all about fun, either. There have been times when we took a day off to clean the house. Listen, when presented with those choices, I usually have very willing helpers on the cleaning thing. Sometimes you have to get caught up for your family's sanity. And don't forget about sick days. Those need to be expected as well.
Having that flexibility is a great blessing of homeschool, but you need to think it out ahead of time. Families that take too many days off find themselves schooling through the summer when they didn't intend to. Morale can get pretty low the further behind everyone gets. So plan those flex days in your schedule, work ahead when you can, and enjoy some days off---no matter the weather.