DD1 (nearly 4) is seriously cautious. She won't contemplate going down a slide, or climb a climbing frame. After we had ice on the garden path last year, it took months for her to walk on the path again instead of the grass. She won't use her scooter.
She is getting better though, and some things (going high on swings, jumping on a trampoline and even riding a pony) don't bother her at all.
She was only persuaded to try sledging when she saw her baby sister (14 months) trying it. After a LOT of coaxing she finally agreed to sit on the sledge, then eventually managed to go down a short slope on her own.
Don't worry about nursery/pre-school. They have so many different things to do, she'll doubtless find something she feels comfortable with and that will provide her with a platform for trying other, more adventurous stuff.
Lots of children that were very shy at first (one for quite a while) when they started at the local pre-school now seem like different children - much more outgoing.
DD1 has her best friend. She tends not to play with the others much when her best friend isn't there too, but has a fab time anyway.