download RDS snapshot

You can't download an RDS snapshot. You can however connect to it and export your databases. Downgrading your instance should not affect connectivity unless you had set up your security groups incorrectly (Opening ports to an IP instead of another security group).

I use:

pg_dump -v -h RDS_URL -Fc -o -U username dbname > your_dump.sql

The accepted answer is not up-to-date anymore. Instead of using command line tools, you can use the AWS console.

Navigate to RDS -> Snapshots -> Manual/System ->

Select Snapshot -> Actions -> Export to S3

Going through S3 is common in most production environments, as you won't have direct access to the DB instance.

In addition to datasage answer.

As an option for production instance you can create a readonly replica in RDS and make dumps from this replica. You could avoid freezing of production DB this way.

We use this scheme for PostgreSQL + pg_dump. Hope it will be helpful to somebody else too.