I'm from Ireland and it can rain any time of the day or night, almost 365 days of the year. I carry an umbrella with me every day when I'm out and about.
Umbrellas are really only useful when there is rain with no wind or very light wind. As I have lived all my life in countries with rain, I am used to using an umbrella with wind and know how to angle it so that it does not blow inside out. However once the wind gets too much I don't use my umbrella and will either get wet or have a coat / jacket with a hood.
I have also used an umbrella in
Disneyland California to shade from the sun. I would advise a small umbrella, which is handbag size. I would not bring a large golf umbrella into the parks.
I would also advise not spending alot of money on an umbrella. I would not spend any more than $10. A small cheap umbrella will fold easily and be able to manage on rides and when you go indoors.
I also always carry a plastic bag. When I go inside shops and restaurants when it is raining, I can fold down the umbrella and put it into the plastic bag and put it in my backpack or handbag. This way I'm not dripping a wet umbrella all over the floor.
For rain in the parks I would bring the umbrella but also wear a waterproof jacket with a hood.