Yes. There are also assistive devices like tricycles, mobility scooters and canta (enclosed microcars).

And bikeable neighbourhood also tend to be a lot more walkable.

And the netherlands have extensive public transportation networks

> Are they trapped at home?

Much less so than in the US, as they don’t need the ability to drive to get out. They are also significantly less dangerous to themselves and others, as they don't need to keep driving way past the age where they should really stop.

> What about the weather? How is biking in the rain or snow?

As they say in Scandinavia, climate is a clothing concern. Biking in the rain is a habit. It doesn’t snow that much in the Netherlands, but Finns do just fine (NJB has a video on Oulu, Finland, where people cycle year round and there’s 10~20 inches of snow from January to March).