Yes, they are open every day. The crowds are usually small because of the rain. If you don't mind the rain it might be a great day to go. Every time I have gone on a rainy day has be great, small crowds, and no lines. But it is a very busy time of year so it may be busy.
Disneyland doesnt close for rain. Disney world does because of monsoons hurricanes and severe thunderstorms. Just wear a poncho tennis shoes pants you will be ok. Some indoor attractions may be closed please see here for more information: https://disneyland.disney.go.com/faq/parks/weather/
I believe so. I hope so. They don't close when it is raining usually. We are planning on going there later today to buy a couple Christmas gifts.
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