Hi Cathy!
What a great age to enjoy the characters! My DD and DS were 3 and 4 on their first visit. It was so neat because they both truly believed that all the characters were real...lots of magic!
We rented those strollers several times and REALLY liked them. They also have a few different options, too. We also rented the rain covers which came in super handy. See below
I always feel sorry for people when it rains (and it does quite often in FL) and their strollers get soaked. The kids can actually sit inside the stroller with the covers on....super handy!!
The scooters or
ECVs can be rented at the parks, but it's first come first serve and they're usually gone fairly quickly. There are other places in Orlando that rent and will deliver to the resorts. Unfortunately you can't load an
ECV on the train unless that's changed.
The parks have been known to close

When we were there last Christmas, or actually the 27th- 29th, none of the parks closed. You just never know.