It's possible to create one and when you google "arduino hydroponics", you'll find a lot of examples.
In it's simplest form you would need an Arduino, real time clock chip, relay and a few extra components to create a watering system which you can configure by PC using an USB-cable. It's possible to do much more though, from adding buttons and LCD-display (so you won't need a computer), to a professional project with tons of sensors and actuators used in agriculture. If you want to, you can have it send messages and giving you the possibility to change settings over the internet, the sky... is the limit.
Since you don't have much experience with electronics it may be advisable to follow Arduino's tutorial though, which gives you some insight on how most common electronic components work and how you can integrate them in a project. When you create a project, it usually is best to learn how each different part basically works and how you can use it with the micro controller. After that you can start combining parts/code and work towards the end result you're looking for.
Looking at projects done before will give you more info and is certainly advisable, but I wouldn't pick and copy a project too fast. If it is a bit advanced and doesn't exactly do what you want to, it may be quite a job to get the knowledge of all parts used, how they're addressed in programming and how to change the program of someone else to your specifications.